Frontend should consume GET /api/providers instead of maintaining a manual provider table

[lfnovo]

Context

PR #1075 introduced a single backend provider registry (open_notebook/ai/provider_registry.py) and a GET /api/providers endpoint exposing name, display name, modalities, docs URL and env-configured status. The frontend still hardcodes its own copy in frontend/src/lib/providers.tsx (ALL_PROVIDERS, PROVIDER_MODALITIES, PROVIDER_DOCS), kept in sync only by a backend test that regex-parses the .tsx file (tests/test_credential_provider_validation.py) — which already broke once when the table moved files (see #1065).

Proposal

• Fetch provider metadata from GET /api/providers (react-query hook, cached)
• Keep only genuinely frontend-only presentation data locally (icons)
• Delete the regex-based cross-check test once the manual table is gone

Outcome

Adding a provider becomes: registry entry + SupportedProvider Literal (enforced by test). Zero frontend edits.

[lfnovo]

Design settled (maintainer discussion, 2026-07-12), two decisions on top of the proposal:

1. The backend registry owns display order. GET /api/providers returns PROVIDERS.values() in declaration order — verify it matches the current curated ALL_PROVIDERS order and adjust the registry declaration if needed (trivial backend tweak, not a new field).
2. A fallback icon is mandatory for providers the backend knows but the frontend has no icon for — otherwise the "zero frontend edits to add a provider" outcome silently breaks.

Also settled: aggressive caching (the list only changes on deploy — session-length staleTime), a proper loading/error state on the settings surfaces, and deleting the regex-based cross-check test (the backend SupportedProvider Literal test keeps covering what matters).