Merge branch 'stack/agent-profiles-3-wire' into stack/agent-profiles-5-web-ui

The Client API carrier's `agentPresets` member was the one member of its class
without an `IApiClient[...]` annotation. Inferring it inlined `AgentPresetEntry`
into the emitted declaration by the specifier TS picks — the host `index.ts` —
dragging the whole gateway, and with it the host `Context` merges, into every
Client program importing the carrier. Annotated like its siblings.

`ApiRemoteAgentOptions.setup` now takes the inspected session rather than its
header alone: this layer resolves a resumed session's preset from the LOG,
because a session that switched while blank ran its turns under the newer
composition and the header is written once at creation.

Conflicts:
	apps/web/tests/snapshots/*/*.expected.md
	packages/client/ui-conversation/src/client/skeleton/InputBar.tsx
	packages/host/apiproxy/src/api-proxy.ts
	scripts/doc-budgets.manifest.json

packages/host/apiproxy/src/api/sessions.ts

@@ -117,6 +117,15 @@ export interface ModelCatalogFailure {
 export interface SessionModels {
   /** Target selected for the session's next assembled step. */
   current: ModelTarget
+  /**
+   * Whether an adapter currently serves `current.provider`, and therefore
+   * whether this session can start a turn at all. Deliberately NOT derivable
+   * from `groups`: catalog membership is advisory, so a route serving a model
+   * it stopped advertising is absent from the groups yet perfectly usable,
+   * while a route whose adapter is gone can serve nothing. A surface that
+   * blocks input must read this rather than the groups.
+   */
+  routable: boolean
   /** Successfully loaded provider groups. */
   groups: ModelProviderGroup[]
   /** Provider-local failures; successful groups remain usable. */