Aggregate projection column types depend on type-affecting session settings (e.g. `cast_keep_nullable`), diverging between declaration, write and read

🕵 Filed as the tracking issue for the aggregate-projection carrier found during the review of https://github.com/ClickHouse/ClickHouse/pull/109196 (analysis and measurements by @groeneai in that PR's review thread). That PR pins `MergeTree` key and skip-index expression types to the server settings baseline, but deliberately does not touch projections, because the projection side needs its own compatibility decision.

### Summary

A projection's column types are derived by re-analyzing its `query_ast` at three stages with three different contexts, and nothing forces them to agree:

| stage | site | context |
|---|---|---|
| declared type | `ProjectionsDescription.cpp` `fillProjectionDescriptionByQuery` | global context |
| write | `ProjectionsDescription.cpp` `calculateByQuery` | the inserting query's context |
| read | `optimizeUseAggregateProjection.cpp` | the reading query's context |

Any type-affecting session setting (for example `cast_keep_nullable`) therefore produces a divergence.

### Reproducer

With `PROJECTION p (SELECT CAST(x AS UInt32) AS k, count() GROUP BY k)` over a `Nullable(UInt32)` column `x`:

- setting on at `INSERT`: `Bad cast from type DB::ColumnNullable to DB::ColumnVector` — logical error (exception in release builds, abort in debug/sanitizer builds) in `writeProjectionPartImpl`;
- setting on at read, projection declared `UInt32`: `Bad cast from type DB::ColumnVector to DB::ColumnNullable` in `Aggregator::mergeStreamsImpl`. Reproduced on 26.8.1.1 unmodified. `EXPLAIN header = 1` shows it without any fault: `Aggregating` claims `Nullable(UInt32)` while `ReadFromMergeTree (p)` emits `UInt32`.

Also, `CREATE TABLE` under `cast_keep_nullable = 1` with such a projection succeeds and the first `INSERT` under default settings then fails; and an unrelated `ALTER ... SETTINGS cast_keep_nullable = 1` on such a table is rejected with `Cannot apply ALTER because it breaks projection` (fails closed, no metadata corruption).

### Why the narrow fixes do not work

1. Pinning the setting on the projection `SELECT` (in `ASTProjectionSelectQuery::cloneToASTSelect`, next to the existing `aggregate_functions_null_for_empty` and `transform_null_in` pins) fixes the `INSERT` abort, but a table created while the setting was a profile default already has a projection part whose `columns.txt` records `Nullable(UInt32)`; the pinned derivation then yields `UInt32` and the read fails on a table that worked before (measured: same data directory, old binary reads it correctly, pinned binary fails).
2. Converting the projection header at read time, the way the `DISTINCT` branch already does in `optimizeUseAggregateProjection.cpp`, does not transplant to the aggregating branch: it feeds intermediate aggregate states through `requestOnlyMergeForAggregateProjection`, which rewrites the key column to the expected output type with no conversion, and the `Nullable` to non-`Nullable` direction has no lossless answer.

The proper fix is what https://github.com/ClickHouse/ClickHouse/pull/109196 does for keys and skip indexes: resolve the projection expression against a stable settings baseline, applied consistently to declaration, calculation and projection analysis — plus a compatibility decision (and likely a `SettingsChangesHistory` entry) for tables that already persisted setting-dependent projection column types, so that canonicalizing at load does not convert a failed write into a failed `ATTACH`.

Related: https://github.com/ClickHouse/ClickHouse/pull/109196
Related: https://github.com/ClickHouse/ClickHouse/issues/109181
Related: https://github.com/ClickHouse/ClickHouse/issues/115237

Start with ProjectionsDescription.cpp, especially fillProjectionDescriptionByQuery and calculateByQuery, then trace projection analysis in optimizeUseAggregateProjection.cpp. Reproduce the cast_keep_nullable cases and compare declaration, write, and read types. Done means a decided compatibility approach and consistent handling for new and already persisted projection types, with regression coverage.

Written by the indexing model from the issue text.