fix(state): enforce write patience during lock acquisition

[RonLi79]

Summary

Make _execute_write()'s application-level patience_s budget authoritative for SQLite write-lock acquisition.

SessionDB keeps the existing 1-second SQLite timeout for direct connection operations. During BEGIN IMMEDIATE, it now snapshots PRAGMA busy_timeout, temporarily sets it to 0, and restores the original value in finally. The randomized application retry loop therefore owns the complete wall-clock budget without leaking a fail-fast timeout to later connection users.

Root cause

The writer connection is opened with a native SQLite busy timeout, while some application write classes use a shorter patience budget (notably 0.5 seconds for S1 activity writes). BEGIN IMMEDIATE could block inside SQLite's busy handler before _execute_write() regained control to check its deadline. The configured application budget was therefore not end-to-end enforceable.

Changes

• Snapshot and restore the connection's existing PRAGMA busy_timeout around write-lock acquisition.
• Set busy_timeout=0 only for BEGIN IMMEDIATE, so lock contention fails fast into the existing deadline-bounded jitter loop.
• Use a local checked connection reference for the full transaction.
• Add regression tests proving timeout restoration after both a successful write and exhausted lock patience.

Verification

Fresh evidence on rebased commit c22367383:

• 15 passed — tests/state/test_write_lock_patience.py plus tests/gateway/test_watchdog_review_76354.py
• 40 passed — complete tests/state plus the gateway watchdog regression
• ruff check hermes_state.py tests/state/test_write_lock_patience.py — clean
• py_compile for implementation and test — clean
• git diff --check upstream/main...HEAD — clean
• Manual probe: a non-default busy_timeout=73ms is restored after both success and lock exhaustion

The pre-fix release candidate reproduced the short-budget failures at roughly 3.7–4.1 seconds despite a 0.5-second budget. The patched snapshot keeps the existing retry/error semantics while enforcing the configured wall-clock deadline.

Independent review

Read-only diff review with Codex gpt-5.3-codex-spark: APPROVE, no blockers. Claude Fable was attempted first but its OAuth session was expired; no Fable verdict is claimed.

[RonLi79]

Rebased onto current upstream/main and added explicit busy_timeout restoration regressions. Fresh local gates: 15/15 focused and 40/40 complete state/watchdog tests, plus Ruff, py_compile, and diff-check. The PR currently has no instantiated check suite; please approve the fork workflow and review when convenient.