[Enhancement] Pass refresh signal from registry refresh button to API (blocked by toolhive#5266)

Context

PR #2216 added a Refresh button to the Registry page (visible for custom registries) with a tooltip showing Source and Updated (the upstream last_updated timestamp). The button currently calls refetch() on the React Query hooks for GET /api/v1beta/registry/default and GET /api/v1beta/registry/default/servers.

Problem

The button is already in place, but for custom registries of type api / url the backend caches data in memory for 1 hour with no way for HTTP clients to bypass it. Clicking refresh fires the same GET requests again, the backend returns cached data, and last_updated does not change. The button works for local_path (file re-read every GET) but is effectively a no-op for api/url.

Tracked upstream: stacklok/toolhive#5266

What needs to change here

Once stacklok/toolhive#5266 lands, the refresh callback in renderer/src/routes/(registry)/-registry.route.tsx needs to pass the cache-bypass signal to the API. The exact shape depends on which option toolhive ships:

• POST /api/v1beta/registry/{name}/refresh endpoint (option 1 in upstream issue) → call the new endpoint before the existing refetch()s.
• ?refresh=true query param on the existing GETs → pass it through the generated client options.
• Cache-Control: no-cache header → set on the request headers for the refresh path only.

In all cases the button itself does not change — only what the refresh callback in -registry.route.tsx (lines 82–86) does before/during the refetch.

Tasks

• Wait for stacklok/toolhive#5266 to ship and confirm the chosen API shape.
• Regenerate the OpenAPI client (pnpm run generate-client).
• Update the refresh callback in renderer/src/routes/(registry)/-registry.route.tsx to pass the new signal.
• Surface backend errors (502/504 if upstream unreachable) via toast.
• Update / extend tests in renderer/src/routes/__tests__/registry.test.tsx.

Acceptance criteria

• Clicking Refresh for a custom registry of type api/url returns fresh data from upstream (verify by changing the upstream registry and confirming the tooltip's Updated moves forward after a click).
• Existing behavior for local_path is preserved.
• Upstream failure (502/504) is surfaced to the user, not silently swallowed.

Dependencies

• Blocked by stacklok/toolhive#5266

References

• PR that added the button + tooltip: #2216
• Upstream issue: stacklok/toolhive#5266

Wait for stacklok/toolhive#5266 and confirm the cache-bypass API shape, then run pnpm run generate-client. Update the refresh callback in renderer/src/routes/(registry)/-registry.route.tsx, especially lines 82–86, and extend renderer/src/routes/tests/registry.test.tsx. Done means custom api/url registries refresh, local_path behavior remains unchanged, and upstream 502/504 errors appear in a toast.