feat(lsp,cwd): LSP integration + per-conversation cwd; fix cache-warming cache bust

LSP + per-conversation CWD feature:
- new bundled `lsp` extension: hand-rolled JSON-RPC codec (framing/rpc), lazy
  one-server-per-(serverID,root), per-cwd config resolution, on-demand `lsp` tool
- `conversation-store`: getCwd/setCwd (cwdKey); `session-orchestrator` defaults a
  turn's cwd from the store
- `transport-http`: cwd + lsp status endpoints; wire types in transport-contract
- host-bin: register lsp; config wiring

Cache-warming fix (the warm read 0% on the first reheat after a message):
- warm assembled tools under a different cwd than the real turn (a reheat sends no
  cwd, and the warm service had no store fallback). The skills filter rewrites the
  cwd-sensitive `load_skill` description, so the tools block — the first bytes of
  the prompt-cache prefix — diverged and the cache missed entirely. Warm now
  resolves cwd as opts.cwd ?? conversationStore.getCwd(), mirroring handleMessage.
- capture warm sends as `provider.request` spans flagged `warm:true` (thread a
  child logger into providerOpts) so warm vs real bodies are diffable (obs §3.1).
- kernel logger: span-close now merges child-bound attrs like span-open, so a
  `warm:true` query finds the closed span (with usage/status), not just the open.

Tests: warm forwards a warm-flagged logger; warm falls back to stored cwd; logger
open/close attr consistency. Full suite green (873).

1 files changed, 43 insertions, 0 deletions

diff --git a/packages/transport-contract/src/index.ts b/packages/transport-contract/src/index.ts
index 95111ae..f0e50f8 100644
--- a/packages/transport-contract/src/index.ts
+++ b/packages/transport-contract/src/index.ts
@@ -154,6 +154,49 @@ export interface ThroughputResponse {
 	readonly models: readonly ThroughputModelStat[];
 }
 
+// ─── Per-conversation working directory (cwd) ─────────────────────────────────
+
+/** Response of `GET /conversations/:id/cwd`. `cwd` is null when never set. */
+export interface CwdResponse {
+	readonly conversationId: string;
+	readonly cwd: string | null;
+}
+
+/** Body of `PUT /conversations/:id/cwd`. */
+export interface SetCwdRequest {
+	readonly cwd: string;
+}
+
+// ─── Per-conversation LSP status ──────────────────────────────────────────────
+
+/** The connection state of a single language server for a workspace. */
+export type LspServerState = "connected" | "starting" | "error" | "not-started";
+
+/** One language server's status as reported to the frontend. */
+export interface LspServerInfo {
+	/** Stable server id, e.g. "typescript", "luau-lsp". */
+	readonly id: string;
+	/** Human-readable display name. */
+	readonly name: string;
+	/** The resolved workspace root the server is (or would be) rooted at (absolute). */
+	readonly root: string;
+	/** File extensions this server handles, e.g. [".ts", ".tsx"] or [".luau"]. */
+	readonly extensions: readonly string[];
+	/** Current connection state. */
+	readonly state: LspServerState;
+	/** Present only when `state === "error"`: a short human-readable reason. */
+	readonly error?: string;
+}
+
+/** Response of `GET /conversations/:id/lsp`. */
+export interface LspStatusResponse {
+	readonly conversationId: string;
+	/** The conversation's persisted cwd, or null if unset (then `servers` is empty). */
+	readonly cwd: string | null;
+	/** The language servers configured for `cwd` and their live state. */
+	readonly servers: readonly LspServerInfo[];
+}
+
 /**
  * Request body for `POST /chat/warm` — manually trigger a prompt-cache WARMING
  * request for a conversation (e.g. a frontend "warm now" button, or fast tests