fix: update UI connection status after OAuth authorization

[bartmichalak]

Description

• Show connected providers on the pairing page instead of offering re-connection
• Invalidate connections cache on OAuth success page so other views reflect new state

Fixes #310

Checklist

General

• My code follows the project's code style
• I have performed a self-review of my code
• I have added tests that prove my fix/feature works (if applicable)
• New and existing tests pass locally

Backend Changes

You have to be in backend directory to make it work:

• uv run pre-commit run --all-files passes

Frontend Changes

• pnpm run lint passes
• pnpm run format:check passes
• pnpm run build succeeds

Testing Instructions

WIP

Screenshots

WIP

Additional Notes

NA

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[railway-app]

🚅 Deployed to the open-wearables-pr-555 environment in Open Wearables

Service	Status	Web	Updated (UTC)
frontend	✅ Success (View Logs)	Web	Mar 5, 2026 at 8:20 am
celery-flower	✅ Success (View Logs)	Web	Mar 5, 2026 at 8:20 am
celery-beat	✅ Success (View Logs)		Mar 5, 2026 at 8:20 am
backend	✅ Success (View Logs)	Web	Mar 5, 2026 at 8:20 am
celery-worker	✅ Success (View Logs)		Mar 5, 2026 at 8:20 am