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/tests/client-handler.spec.ts

@@ -46,6 +46,7 @@ function scriptedApi(overrides: {
       }),
       models: r => ok(r, {
         current: { provider: 'deepseek-official', model: 'deepseek-v4-flash' },
+        routable: true,
         groups: [],
         failures: [],
       }),