fix(app): restore custom provider creation on v2 - #52653

Issue for this PR

Closes #51330
Closes #50650

Type of change

• Bug fix

What does this PR do?

The custom-provider form always threw an unavailable error and still built V1 config. Restore saving through V2: write native provider config, store API keys separately through credential.create, refresh the selected location, and show the new models.

Extend the existing experimental global config patch to accept provider entries by ID without replacing other providers or JSONC comments. Config writes reload the owning config before returning. Regenerate the client.

How did you verify your code works?

• bun run check passed.
• Server config tests passed (2 tests), covering provider writes/removal, JSONC preservation, separate credentials, and provider availability after activation settles.
• Existing custom-provider form tests passed (2 tests).
• Playwright settings regression passed: complete the real form, verify config and credential requests, and verify the new model is enabled.
• Separate bun typecheck:e2e remains blocked by existing errors in e2e/performance/terminals/probe.ts and e2e/performance/timeline/session-timeline-stream-probe.ts.

Screenshots / recordings

No visual layout changes; the existing form now saves instead of showing an error. Covered by the browser regression.

Checklist

• I have tested my changes locally
• I have not included unrelated changes in this PR