fix: make Biome validation commands read-only

[abhinavkr26104]

Closes #1448

Summary

• make root format-lint validation read-only
• make apps/web lint validation read-only
• add explicit format-lint:fix and lint:fix commands for intentional Biome fixes

Validation

• confirmed both package manifests parse successfully
• ran bun run format-lint
• Biome reported existing formatting/lint violations and printed No fixes applied
• confirmed the command did not introduce content changes beyond this PR’s script updates

[suryaraj09]

Review

The core change is correct and I verified it against a fresh checkout of main:

• biome check without --write is read-only (file hashes unchanged after running)
• It exits non-zero on violations, meeting fix: make lint and format validation commands non-mutating #1448's acceptance criteria
• CI is unaffected — it already uses bunx biome ci --changed (read-only)

However, #1463 already covers this exact change and more: it makes the same two package.json edits, plus updates claude-auto-fix-ci.yml (the auto-fix bot prompt must switch to format-lint:fix, otherwise it would run a now-read-only command and fail to apply fixes) and documents the new read-only vs :fix split in CLAUDE.md / CONTRIBUTING.md.

Suggest closing this as a duplicate of #1463 to avoid two conflicting script changes landing on main.

Shared gap worth tracking (raised on #1463 too): the codebase currently has 652 pre-existing Biome errors (mostly config-file formatting, plus stale biome.json schema 2.2.2 vs Biome 2.4.6 → deserialize errors), so bun run format-lint will fail on a fresh checkout until a follow-up cleanup lands.