Connections from PostgreSQL connection pools are not reused within a single query or other concurrent executing queries

**ClickHouse version 24.2.1**

**Describe the unexpected behaviour**
When running a query that uses `PostgreSQLPoolWithFailover` connections to PostgreSQL stays "idle" after execution on PG side (till query on CH side executes) and are not reused within the same query or another query that uses `PostgreSQLPoolWithFailover`. My conclusions are:

- each query with postgresql table functions has it own `PostgreSQLPoolWithFailover` (created at start of the query),
- for all PostgreSQL engine tables there is one `PostgreSQLPoolWithFailover` created at the server startup,
- connection from `PostgreSQLPoolWithFailover` when query is executed is not reused within query nor other executing CH queries,
- connection from `PostgreSQLPoolWithFailover` when query is executed stays idle after execution on pg side (connected but not doing any work) till the end of the CH query.

**How to reproduce**
Create a table on PG side:

```
CREATE TABLE test (
a INTEGER PRIMARY KEY,
b INTEGER NOT NULL,
c INTEGER NOT NULL,
d INTEGER NOT NULL
);

INSERT INTO test SELECT a, a, a, a FROM generate_series(1, 10, 1) a;
```

Create a PostgreSQL engine table on ClickHouse:
```
CREATE TABLE default.test_pg (
`a` Int64,
`b` Int64,
`c` Int64,
`d` Int64
)
ENGINE = PostgreSQL('127.0.0.1:5432', 'test', 'test', 'test', 'test');
```

Execute a query on CH side (default for `postgresql_connection_pool_size` is 16):
```
SELECT * FROM (SELECT * FROM test_pg LIMIT 10) t
/*this will artificaly slow down SELECT*/
JOIN (SELECT sleepEachRow(0.000001), 1 n FROM numbers(10e7)) s ON t.a = s.n
JOIN (SELECT * FROM test_pg) x1 ON x1.a=t.a
JOIN (SELECT * FROM test_pg) x2 ON x2.a=t.a
JOIN (SELECT * FROM test_pg) x3 ON x3.a=t.a
JOIN (SELECT * FROM test_pg) x4 ON x4.a=t.a
JOIN (SELECT * FROM test_pg) x5 ON x5.a=t.a
JOIN (SELECT * FROM test_pg) x6 ON x6.a=t.a
JOIN (SELECT * FROM test_pg) x7 ON x7.a=t.a
JOIN (SELECT * FROM test_pg) x8 ON x8.a=t.a
JOIN (SELECT * FROM test_pg) x9 ON x9.a=t.a
JOIN (SELECT * FROM test_pg) x10 ON x10.a=t.a
JOIN (SELECT * FROM test_pg) x11 ON x11.a=t.a
JOIN (SELECT * FROM test_pg) x12 ON x12.a=t.a
JOIN (SELECT * FROM test_pg) x13 ON x13.a=t.a
JOIN (SELECT * FROM test_pg) x14 ON x14.a=t.a
JOIN (SELECT * FROM test_pg) x15 ON x15.a=t.a
JOIN (SELECT * FROM test_pg) x16 ON x16.a=t.a;

Received exception from server (version 24.2.1):
Code: 614. DB::Exception: Received from localhost:9000. DB::Exception. (POSTGRESQL_CONNECTION_FAILURE)
```

```
SELECT pid, usename, application_name, client_hostname, client_port, backend_start, state, query_id FROM pg_stat_activity
pid | usename | application_name | client_hostname | client_port | backend_start | state | query_id
-------+----------+------------------+-----------------+-------------+-------------------------------+--------+----------
1036 | | | | | 2024-04-10 09:43:05.76965+02 | |
1037 | postgres | | | | 2024-04-10 09:43:05.769938+02 | |
54552 | test | | | 39786 | 2024-04-24 12:05:43.062189+02 | idle |
54617 | test | | | 42420 | 2024-04-24 12:06:01.210384+02 | idle |
56469 | test | | | 35802 | 2024-04-25 15:06:44.404462+02 | idle |
56468 | test | | | 35796 | 2024-04-25 15:06:44.388475+02 | idle |
56467 | test | | | 35786 | 2024-04-25 15:06:44.372918+02 | idle |
56466 | test | | | 35782 | 2024-04-25 15:06:44.360284+02 | idle |
56465 | test | | | 35770 | 2024-04-25 15:06:44.34932+02 | idle |
56464 | test | | | 35764 | 2024-04-25 15:06:44.336819+02 | idle |
56470 | test | | | 35808 | 2024-04-25 15:06:44.420517+02 | idle |
56471 | test | | | 35814 | 2024-04-25 15:06:44.439634+02 | idle |
56463 | test | | | 35760 | 2024-04-25 15:06:44.32513+02 | idle |
56462 | test | | | 35744 | 2024-04-25 15:06:44.3129+02 | idle |
56461 | test | | | 35738 | 2024-04-25 15:06:44.302739+02 | idle |
56460 | test | | | 35736 | 2024-04-25 15:06:44.291444+02 | idle |
56459 | test | | | 35734 | 2024-04-25 15:06:44.281793+02 | idle |
```

You can the same querytwice from different connections, one will execute while other will fail with the same exception message as above.
```
SELECT * FROM (SELECT * FROM test_pg LIMIT 10) t
/*this will artificaly slow down SELECT*/
JOIN (SELECT sleepEachRow(0.000001), 1 n FROM numbers(10e7)) s ON t.a = s.n
JOIN (SELECT * FROM test_pg) x1 ON x1.a=t.a
JOIN (SELECT * FROM test_pg) x2 ON x2.a=t.a
JOIN (SELECT * FROM test_pg) x3 ON x3.a=t.a
JOIN (SELECT * FROM test_pg) x4 ON x4.a=t.a
JOIN (SELECT * FROM test_pg) x5 ON x5.a=t.a
JOIN (SELECT * FROM test_pg) x6 ON x6.a=t.a
JOIN (SELECT * FROM test_pg) x7 ON x7.a=t.a
JOIN (SELECT * FROM test_pg) x8 ON x8.a=t.a
JOIN (SELECT * FROM test_pg) x9 ON x9.a=t.a
JOIN (SELECT * FROM test_pg) x10 ON x10.a=t.a;

← Progress: 9.09 million rows, 72.74 MB (963.48 thousand rows/s., 7.71 MB/s.) █████████▉ (0.0 CPU) 9%

SELECT * FROM (SELECT * FROM test_pg LIMIT 10) t
/*this will artificaly slow down SELECT*/
JOIN (SELECT sleepEachRow(0.000001), 1 n FROM numbers(10e7)) s ON t.a = s.n
JOIN (SELECT * FROM test_pg) x1 ON x1.a=t.a
JOIN (SELECT * FROM test_pg) x2 ON x2.a=t.a
JOIN (SELECT * FROM test_pg) x3 ON x3.a=t.a
JOIN (SELECT * FROM test_pg) x4 ON x4.a=t.a
JOIN (SELECT * FROM test_pg) x5 ON x5.a=t.a
JOIN (SELECT * FROM test_pg) x6 ON x6.a=t.a
JOIN (SELECT * FROM test_pg) x7 ON x7.a=t.a
JOIN (SELECT * FROM test_pg) x8 ON x8.a=t.a
JOIN (SELECT * FROM test_pg) x9 ON x9.a=t.a
JOIN (SELECT * FROM test_pg) x10 ON x10.a=t.a;

Elapsed: 10.325 sec.

Received exception from server (version 24.2.1):
Code: 614. DB::Exception: Received from localhost:9000. DB::Exception. (POSTGRESQL_CONNECTION_FAILURE)
```

**Expected behavior**
Connections to PostgreSQL are reused within the same query and other queries executing at the same time.

**Error message and/or stacktrace**

```
Query id: 6939316a-d663-448a-87e1-5b2485aeb0be

[LAPTOP-ASLS2SOJ] 2024.04.25 15:47:45.570762 [ 53864 ] {6939316a-d663-448a-87e1-5b2485aeb0be} executeQuery: (from 127.0.0.1:53862) SELECT * FROM (SELECT * FROM test_pg LIMIT 10) t /*this will artificaly slow down SELECT*/
JOIN (SELECT sleepEachRow(0.000001), 1 n FROM numbers(10e7)) s ON t.a = s.n (stage: Complete)
[LAPTOP-ASLS2SOJ] 2024.04.25 15:47:45.571260 [ 53864 ] {6939316a-d663-448a-87e1-5b2485aeb0be} ContextAccess (default): Access granted: SELECT(a, b, c, d) ON default.test_pg
[LAPTOP-ASLS2SOJ] 2024.04.25 15:47:45.571674 [ 53864 ] {6939316a-d663-448a-87e1-5b2485aeb0be} ContextAccess (default): Access granted: SELECT(a, b, c, d) ON default.test_pg
[LAPTOP-ASLS2SOJ] 2024.04.25 15:47:45.572093 [ 53864 ] {6939316a-d663-448a-87e1-5b2485aeb0be} InterpreterSelectQuery: FetchColumns -> Complete
[LAPTOP-ASLS2SOJ] 2024.04.25 15:47:45.572213 [ 53864 ] {6939316a-d663-448a-87e1-5b2485aeb0be} TableJoin: Infer supertype for joined columns. Left: [a : Int64 -> Int64], Right: [n : UInt8 -> Int64]
[LAPTOP-ASLS2SOJ] 2024.04.25 15:47:45.572376 [ 53864 ] {6939316a-d663-448a-87e1-5b2485aeb0be} HashJoin: Keys: [(a) = (materialize(_CAST(n, Int64)))], datatype: EMPTY, kind: Inner, strictness: All, right header: n UInt8 Const(size = 0, UInt8(size = 1)), sleepEachRow(0.000001) UInt8 UInt8(size = 0), materialize(_CAST(n, Int64)) Int64 Int64(size = 0)
[LAPTOP-ASLS2SOJ] 2024.04.25 15:47:45.572657 [ 53864 ] {6939316a-d663-448a-87e1-5b2485aeb0be} ContextAccess (default): Access granted: SELECT(a, b, c, d) ON default.test_pg
[LAPTOP-ASLS2SOJ] 2024.04.25 15:47:45.572749 [ 53864 ] {6939316a-d663-448a-87e1-5b2485aeb0be} StoragePostgreSQL (test_pg): Query: SELECT "a", "b", "c", "d" FROM "test"
[LAPTOP-ASLS2SOJ] 2024.04.25 15:47:50.572960 [ 53864 ] {6939316a-d663-448a-87e1-5b2485aeb0be} PostgreSQLConnectionPool: Unable to fetch connection within the timeout
[LAPTOP-ASLS2SOJ] 2024.04.25 15:47:55.573163 [ 53864 ] {6939316a-d663-448a-87e1-5b2485aeb0be} PostgreSQLConnectionPool: Unable to fetch connection within the timeout
[LAPTOP-ASLS2SOJ] 2024.04.25 15:47:55.573482 [ 53864 ] {6939316a-d663-448a-87e1-5b2485aeb0be} HashJoin: Join data is being destroyed, 8192 bytes and 0 rows in hash table
[LAPTOP-ASLS2SOJ] 2024.04.25 15:47:55.574491 [ 53864 ] {6939316a-d663-448a-87e1-5b2485aeb0be} executeQuery: Code: 614. DB::Exception. (POSTGRESQL_CONNECTION_FAILURE) (version 24.2.1.1598 (official build)) (from 127.0.0.1:53862) (in query: SELECT * FROM (SELECT * FROM test_pg LIMIT 10) t /*this will artificaly slow down SELECT*/
JOIN (SELECT sleepEachRow(0.000001), 1 n FROM numbers(10e7)) s ON t.a = s.n), Stack trace (when copying this message, always include the lines below):

0. DB::Exception::Exception(DB::Exception::MessageMasked&&, int, bool) @ 0x000000000c9a503b in /usr/bin/clickhouse
1. DB::Exception::Exception(PreformattedMessage const&, int) @ 0x000000000f95782c in /usr/bin/clickhouse
2. postgres::PoolWithFailover::get() @ 0x000000001005597b in /usr/bin/clickhouse
3. DB::StoragePostgreSQL::read(std::vector> const&, std::shared_ptr const&, DB::SelectQueryInfo&, std::shared_ptr, DB::QueryProcessingStage::Enum, unsigned long, unsigned long) @ 0x0000000011e669f9 in /usr/bin/clickhouse
4. DB::IStorage::read(DB::QueryPlan&, std::vector> const&, std::shared_ptr const&, DB::SelectQueryInfo&, std::shared_ptr, DB::QueryProcessingStage::Enum, unsigned long, unsigned long) @ 0x0000000011cec8d9 in /usr/bin/clickhouse
5. DB::InterpreterSelectQuery::executeImpl(DB::QueryPlan&, std::optional) @ 0x00000000114c59ce in /usr/bin/clickhouse
6. DB::InterpreterSelectQuery::buildQueryPlan(DB::QueryPlan&) @ 0x00000000114c2f14 in /usr/bin/clickhouse
7. DB::InterpreterSelectWithUnionQuery::buildQueryPlan(DB::QueryPlan&) @ 0x000000001157f3c4 in /usr/bin/clickhouse
8. DB::InterpreterSelectQuery::executeImpl(DB::QueryPlan&, std::optional) @ 0x00000000114c631f in /usr/bin/clickhouse
9. DB::InterpreterSelectQuery::buildQueryPlan(DB::QueryPlan&) @ 0x00000000114c2f14 in /usr/bin/clickhouse
10. DB::InterpreterSelectWithUnionQuery::buildQueryPlan(DB::QueryPlan&) @ 0x000000001157f3c4 in /usr/bin/clickhouse
11. DB::InterpreterSelectWithUnionQuery::execute() @ 0x000000001158043e in /usr/bin/clickhouse
12. DB::executeQueryImpl(char const*, char const*, std::shared_ptr, DB::QueryFlags, DB::QueryProcessingStage::Enum, DB::ReadBuffer*) @ 0x0000000011913c68 in /usr/bin/clickhouse
13. DB::executeQuery(String const&, std::shared_ptr, DB::QueryFlags, DB::QueryProcessingStage::Enum) @ 0x000000001190ea7a in /usr/bin/clickhouse
14. DB::TCPHandler::runImpl() @ 0x000000001294aae9 in /usr/bin/clickhouse
15. DB::TCPHandler::run() @ 0x0000000012962b19 in /usr/bin/clickhouse
16. Poco::Net::TCPServerConnection::start() @ 0x000000001523dbf2 in /usr/bin/clickhouse
17. Poco::Net::TCPServerDispatcher::run() @ 0x000000001523e9f1 in /usr/bin/clickhouse
18. Poco::PooledThread::run() @ 0x0000000015337087 in /usr/bin/clickhouse
19. Poco::ThreadImpl::runnableEntry(void*) @ 0x00000000153356bd in /usr/bin/clickhouse
20. ? @ 0x00007fa5b6cea609
21. ? @ 0x00007fa5b6c0f353

Elapsed: 10.006 sec.

Received exception from server (version 24.2.1):
Code: 614. DB::Exception: Received from localhost:9000. DB::Exception. (POSTGRESQL_CONNECTION_FAILURE)
```