feat(web-search-deepseek): resolve provider options from the settings section

The provider now takes a thunk rather than a value: it projects the
authoritative section per search, so a stored endpoint, model, or key
reference reaches the next call without re-registering the provider — which
would make the seam's provider selection observable as a flicker.

apiKey already carries role('secret'), so the section is safe to describe:
the literal never rides a response in any layer and a configuration surface
learns only that a key is set.

docs/config-catalog.md

@@ -2595,7 +2595,7 @@ export interface Config {
 }
 ```
 
-Source: [`packages/web/web-search-deepseek/src/index.ts:44`](../packages/web/web-search-deepseek/src/index.ts)
+Source: [`packages/web/web-search-deepseek/src/index.ts:46`](../packages/web/web-search-deepseek/src/index.ts)
 
 ## `@deepseek-ai/dsh-web-search-exa`