Desktop's web picker had no way to send one capability through the Nous
Tool Gateway while the other used your own key. "Use for Search/Extract"
on the Nous Subscription row wrote the row's vendor string (firecrawl)
into web.<cap>_backend, which the runtime reads as BYOK Firecrawl: the
gateway was never used, and the managed and BYOK rows lit up together.
- The managed per-capability pick now stores `nous`; search/extract
dispatch, the registry and the Firecrawl client resolve the route per
capability (search: managed Perplexity, extract: managed Firecrawl).
- A whole-toolset Nous pick clears stale per-capability pins (they
outranked the new selection).
- /api/tools/toolsets/web/config reports search_via_nous /
extract_via_nous and each row's managed_nous_feature; the panel lights
the right row, labels the route, and refetches after a pick instead of
mirroring the vendor string.
Fixes#100513. Builds on the approach in #100539 by @liuhao1024 and the
self-healing pin clear from #122676 by @praggybuilds.
Co-authored-by: liuhao1024 <sunsky.lau@gmail.com>
Co-authored-by: Murphy (praggybuilds) <praggybuilds@users.noreply.github.com>
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