Unexpected connection close when executing `kill query` on idle connection

## Bug Report

Please answer these questions before submitting your issue. Thanks!

### 1. Minimal reproduce step (Required)

```
session 1:
mysql> show processlist;
+-----------+------+----------------+------+---------+------+------------+------------------+
| Id | User | Host | db | Command | Time | State | Info |
+-----------+------+----------------+------+---------+------+------------+------------------+
| 346030088 | root | 10.2.8.3:48768 | NULL | Query | 0 | autocommit | show processlist |
| 346030086 | root | 10.2.8.3:48696 | NULL | Sleep | 7 | autocommit | NULL |
+-----------+------+----------------+------+---------+------+------------+------------------+
2 rows in set (0.00 sec)

mysql> kill tidb query 346030086;
Query OK, 0 rows affected (0.00 sec)

session 2:
mysql> show processlist;
ERROR 2013 (HY000): Lost connection to MySQL server during query
```

### 2. What did you expect to see? (Required)

The connection for session 2 shouldn't be closed.

### 3. What did you see instead (Required)

The connection is closed and the i/o timeout error is reporterd in TiDB log like the following:
```
[2024/11/29 18:22:02.430 +08:00] [INFO] [server.go:897] [kill] [conn=346030086] [query=true] [maxExecutionTime=false] [runawayExceed=false]
[2024/11/29 18:22:02.431 +08:00] [WARN] [sqlkiller.go:61] ["kill initiated"] ["connection ID"=346030086] [reason="[executor:1317]Query execution was interrupted"]
[2024/11/29 18:22:02.431 +08:00] [INFO] [conn.go:1106] ["read packet timeout, close this connection"] [conn=346030086] [session_alias=] [idle=18.588288003s] [waitTimeout=28800] [error="read tcp 10.2.8.3:26333->10.2.8.3:48696: i/o timeout"]
```

### 4. What is your TiDB version? (Required)

v8.3.0

Reproduce the two-session sequence from the issue on TiDB v8.3.0, then trace the logged paths in server.go:897, sqlkiller.go:61, and conn.go:1106. Compare the idle connection's kill handling with the read-packet timeout path; done means killing the idle query no longer closes session 2 or reports the timeout shown in the log.

Written by the indexing model from the issue text.