ci: expand conditional PostgreSQL validation

[gbaudrit]

Summary

Keep SQLite as the primary CI validation while expanding the optional PostgreSQL job introduced by #109 and preserved by #110 to exercise the Web test suite when storage-relevant files change or the workflow is dispatched manually.

Changes

• Classify PostgreSQL-relevant paths and skip the PostgreSQL job for unrelated pull requests.
• Run the dedicated migration and restart test before the broader Web test suite with PostgreSQL configured globally.
• Categorize PostgreSQL, SQLite-specific, and benchmark tests so each CI phase selects the appropriate coverage.

Validation

• Release build succeeded with 0 warnings and 0 errors.
• Full test suite passed: 602 total, 598 passed, 4 optional integrations skipped, 0 failed.
• PostgreSQL 17 migration and restart test passed: 1/1.
• Web test suite with PostgreSQL storage passed: 183/183.
• PostgreSQL concurrency benchmark passed with 40 operations, 8-way concurrency, 0 errors, and 0 conflicts.
• Documentation and desktop/mobile smoke testing were not applicable because this change only affects CI and test categorization.

Breaking changes

None.