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/components/lanes/__tests__/AddLaneModal.test.tsx

@@ -48,6 +48,8 @@ function laneFixture(over: Partial<Lane> = {}): Lane {
     liveness: "idle",
     detected_stage: null,
     detected_signal: null,
+    slot: null,
+    ports: {},
     ...over,
   };
 }
@@ -59,13 +61,7 @@ const SUGGESTIONS: CwdSuggestion[] = [
 
 function renderModal(over: Partial<React.ComponentProps<typeof AddLaneModal>> = {}) {
   return render(
-    <AddLaneModal
-      open
-      onClose={vi.fn()}
-      onAdded={vi.fn()}
-      cwdSuggestions={SUGGESTIONS}
-      {...over}
-    />
+    <AddLaneModal open onClose={vi.fn()} onAdded={vi.fn()} cwdSuggestions={SUGGESTIONS} {...over} />
   );
 }
 
@@ -100,7 +96,9 @@ describe("AddLaneModal", () => {
     await focusField(user, repoField);
     await user.type(repoField, "/Users/tester/projects/repo");
 
-    await waitFor(() => expect(api.lanes.branches).toHaveBeenCalledWith("/Users/tester/projects/repo"));
+    await waitFor(() =>
+      expect(api.lanes.branches).toHaveBeenCalledWith("/Users/tester/projects/repo")
+    );
     const base = await screen.findByLabelText("Branch to fork from");
     expect(base).toHaveValue("main"); // the repo's current branch is preselected
     expect(screen.getByRole("option", { name: "feat/other" })).toBeInTheDocument();
@@ -143,7 +141,9 @@ describe("AddLaneModal", () => {
         base: "main",
       });
     });
-    expect(onAdded).toHaveBeenCalledWith(expect.objectContaining({ id: 9, status: "provisioning" }));
+    expect(onAdded).toHaveBeenCalledWith(
+      expect.objectContaining({ id: 9, status: "provisioning" })
+    );
     expect(onClose).toHaveBeenCalled();
   });