fix: align Node runtime for node:sqlite

[SergioChan]

Summary

• raise the application runtime floor to Node.js 22.13, the first release where node:sqlite is available without the enablement flag
• pin CI and the embedded DMG runtime through .node-version at Node.js 22.22.0
• verify both the minimum supported runtime and the packaged runtime in GitHub Actions
• make source installers probe the actual DatabaseSync capability before installation
• install the selective SQLite warning filter before loading the Codex state runtime
• update source-install docs and add runtime boundary regressions

Root cause

PR #6 introduced a direct node:sqlite dependency while CI remained on Node.js 22.12.0, where importing that built-in without --experimental-sqlite fails with ERR_UNKNOWN_BUILTIN_MODULE.

Verification

• npm run check — passed (78 JavaScript, 22 shell, 20 Markdown files)
• focused runtime suite on Node.js 22.13.0 — 18/18 passed
• focused runtime suite on packaged Node.js 22.22.0 — 18/18 passed
• Shell syntax, workflow YAML, and git diff --check — passed
• local full suite reached 184/192 passing; the remaining eight native tests are blocked by this Mac's pre-existing toolchain mismatch (Swift 6.2 SDK with Swift 6.1.2 compiler). The GitHub macOS runner is the authoritative full-suite check.