fix(db): install busy_timeout before the connection's first statement (#12394)

getDbInstance() ran PRAGMA journal_mode = WAL as the connection's first statement, before PRAGMA busy_timeout, and openSqliteDatabase() passes no driver-level timeout. A process opening the database while another closed its WAL connection — checkpoint plus WAL delete hold an EXCLUSIVE lock for a few hundred microseconds — therefore died with `database is locked` instead of waiting. That is the flake behind exclusive-connection-leases.test.ts on release/v3.8.51 runs 33525300898 and 33493797519 and on unrelated PR runs.

The second half is worse than the flake: isTransientProbeError matched /SQLITE_BUSY/ against error.message, but both drivers report the plain text `database is locked` and put the code in .code / .errcode. A transient lock during the corruption probe therefore took the corrupt-database path and renamed the file to storage.sqlite.probe-failed-… with "Manual recovery required". The probe now recognises the drivers' real BUSY/PROTOCOL/IOERR signals.

Validated in a combined worktree with all 25 PRs of this batch boarded together: typecheck:core clean, 443/443 node-runner tests plus 14/14 vitest across every test file the batch touches, and check-changelog-integrity, check:cycles (418 files), check:provider-consistency (272 REGISTRY entries, 355 canonical providers), check:docs-counts, check:docs-sync (42 locales) and check-file-size all green.

Thanks @pacocartones.