feat(sqlite): Replace deadpool-sqlite by our own implementation

[Hywan]

🚧 WIP 🚧

This patch replaces deadpool-sqlite by our own implementation in crate::connection. It still uses deadpool but the object manager has a different implementation.

[codecov]

Codecov Report

❌ Patch coverage is 86.11111% with 5 lines in your changes missing coverage. Please review.
✅ Project coverage is 88.61%. Comparing base (3b14184) to head (c3491bf).
⚠️ Report is 2 commits behind head on main.
✅ All tests successful. No failed tests found.

Files with missing lines	Patch %	Lines
crates/matrix-sdk-sqlite/src/connection.rs	90.00%	3 Missing ⚠️
crates/matrix-sdk-sqlite/src/crypto_store.rs	50.00%	0 Missing and 1 partial ⚠️
crates/matrix-sdk-sqlite/src/state_store.rs	75.00%	0 Missing and 1 partial ⚠️

Additional details and impacted files

@@ Coverage Diff @@ ## main #5841 +/- ## ========================================== - Coverage 88.61% 88.61% -0.01%  ========================================== Files 361 362 +1 Lines 102269 102297 +28 Branches 102269 102297 +28 ========================================== + Hits 90627 90646 +19  - Misses 7420 7427 +7  - Partials 4222 4224 +2 

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[codspeed-hq]

CodSpeed Performance Report

Merging #5841 will not alter performance

_{Comparing Hywan:feat-sqlite-custom-pool-manager (c3491bf) with main (3b14184)}

Summary

✅ 50 untouched