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

apps/web/tests/snapshots/markdown-inline-code-links/ui.expected.md

@@ -34,8 +34,8 @@
   - img
 - 'button "Access mode, current: Workspace Write"': Workspace Write
 - text: standard
-- button "Select model":
-  - text: Select model
+- button "Select model, current DeepSeek-V4-Flash":
+  - text: DeepSeek-V4-Flash
   - img
 - button "Send message" [disabled]
 - text: 1 turns · 1 steps LLM {{duration}} Input 0 tok · Output 0 tok