feat(lanes): lane runtime UI, docs, and env additions (A1+A2)

Client-side rendering for the per-lane runtime facts (slot, ports,
database, Redis index, service liveness) added in the server-side
A1/A2 work, plus the doc updates (README, CLAUDE.md, docs/API.md,
client/server READMEs) describing the new profile.env keys, hook
environment contract, and REST endpoints.

client/src/lib/api.ts

@@ -392,6 +392,7 @@ import type {
   Lane,
   LaneCounts,
   LaneGitFacts,
+  LaneRuntime,
   ModelPricing,
   Session,
   SessionDrillIn,
@@ -1932,6 +1933,40 @@ export const api = {
      * readable git repository, which is a normal state rather than an error.
      */
     git: (id: number) => request<LaneGitFacts>(`/lanes/${id}/git`),
+    /**
+     * GET /api/lanes/:id/runtime — the lane's own application stack: slot,
+     * ports, service liveness, and the last boot error.
+     *
+     * Its own endpoint rather than a field on the polled lane list because it
+     * probes ports and stats pid files. Like `/git`, a lane with no profile
+     * answers `available: false` with HTTP 200 — a normal state, not a fault.
+     * @param id The lane id.
+     * @returns {@link LaneRuntime}
+     */
+    runtime: (id: number) => request<LaneRuntime>(`/lanes/${id}/runtime`),
+    /**
+     * POST /api/lanes/:id/up — boot the lane's stack through its profile hooks.
+     * Returns 202: the boot runs in the background and streams progress as
+     * `lane_hook_output`, finishing with a `lane_runtime` message.
+     * @param id The lane id.
+     * @param body `build: false` reuses an existing build.
+     */
+    up: (id: number, body: { build?: boolean } = {}) =>
+      request<{ ok: true; laneId: number }>(`/lanes/${id}/up`, {
+        method: "POST",
+        body: JSON.stringify(body),
+      }),
+    /**
+     * POST /api/lanes/:id/down — stop the lane's stack. Idempotent, and a no-op
+     * for a lane that was never brought up.
+     * @param id The lane id.
+     * @returns The pids stopped and the resulting runtime facts.
+     */
+    down: (id: number) =>
+      request<{ ok: true; killed: number[]; runtime: LaneRuntime }>(`/lanes/${id}/down`, {
+        method: "POST",
+        body: JSON.stringify({}),
+      }),
     /**
      * POST /api/lanes — create a new lane.
      * @param body Optional lane initialization fields.