feat(ai-tools): Settings → AI Tools, Default/Other lane picker, per-run bypass switch (#40 A1)

Settings → Dashboard gains an AI Tools section (installed tools with
Enabled/Disabled and Set default, available ones with a homepage link,
Refresh). useAiTools shares one catalog copy across the app and replaces
LANE_TOOL_LABEL. The Add-lane modal picks Default (<tool>) or Other…; the
router row reads Native (<tool>) and disables AI Router profiles for tools
that cannot use one. The run form gives catalog tools resume and a red
per-run Bypass permissions switch (Codex too). Claude Code / Codex settings
tabs hide while that tool is disabled. The Workspace probes each lane tool's
CLI fresh.

Docs: CLAUDE.md tool/bypass rule, AGENTS.md, LANES.md, API.md, CLI.md,
server/README.md, OpenAPI fragment + regenerated openapi.yaml.

client/src/pages/Workspace.tsx

@@ -56,7 +56,7 @@ import {
 } from "lucide-react";
 import { api } from "../lib/api";
 import type { CwdSuggestion, RunListResponse } from "../lib/api";
-import type { Lane, LaneFeature, ProofFeature, Session, WSMessage, LaneTool } from "../lib/types";
+import type { Lane, LaneFeature, ProofFeature, Session, WSMessage } from "../lib/types";
 import { eventBus } from "../lib/eventBus";
 import { keepIfSame } from "../lib/keepIfSame";
 import {
@@ -175,7 +175,7 @@ function ConsoleArea({
   selectedLaneId: number | null;
   splitView: SplitViewState;
   setLayout: (layout: SplitLayout) => void;
-  binaryStatus: Record<LaneTool, { found: boolean; path: string | null }> | null;
+  binaryStatus: Record<string, { found: boolean; path: string | null }> | null;
   cwdSuggestions: CwdSuggestion[];
   activeRuns: RunListResponse | null;
   externalSessions: Session[];
@@ -296,7 +296,7 @@ export function Workspace() {
   // would otherwise show nothing while two agents are working.
   const [externalSessions, setExternalSessions] = useState<Session[]>([]);
   const [binaryStatus, setBinaryStatus] = useState<Record<
-    LaneTool,
+    string,
     { found: boolean; path: string | null }
   > | null>(null);
   const [cwdSuggestions, setCwdSuggestions] = useState<CwdSuggestion[]>([]);
@@ -394,13 +394,25 @@ export function Workspace() {
     );
   }, [lanes, searchParams, setSearchParams]);
 
+  // Probe the CLI of every tool a lane uses — fresh on the server, so a CLI
+  // installed since the page loaded clears its missing-binary banner. Claude is
+  // always probed: the console's no-lane state runs it.
+  const laneToolsKey = Array.from(new Set(["claude", ...lanes.map((l) => l.tool || "claude")]))
+    .sort()
+    .join(",");
   useEffect(() => {
-    Promise.all([api.run.binary("claude"), api.run.binary("codex"), api.run.binary("antigravity")])
-      .then(([claude, codex, antigravity]) => setBinaryStatus({ claude, codex, antigravity }))
+    const tools = laneToolsKey.split(",");
+    Promise.all(tools.map((tool) => api.run.binary(tool)))
+      .then((found) =>
+        setBinaryStatus(Object.fromEntries(tools.map((tool, i) => [tool, found[i]!])))
+      )
       // Fetch failure (server unreachable, proxy misrouted, etc.) isn't proof
-      // `claude` or `codex` is missing from PATH — leave the probe unresolved rather than
+      // a CLI is missing from PATH — leave the probe unresolved rather than
       // showing a misleading "binary missing" banner for an unrelated fault.
       .catch(() => undefined);
+  }, [laneToolsKey]);
+
+  useEffect(() => {
     api.lanes
       .pipelines()
       .then((r) => setPipelineTemplates(r.pipelines))
@@ -860,7 +872,7 @@ export function Workspace() {
                       </select>
                     )}
                     {/* `agy` has no endpoint to point at a router. */}
-                    {currentLane.tool !== "antigravity" && <LaneRouterRow lane={currentLane} />}
+                    <LaneRouterRow lane={currentLane} />
                     {/* No stage chip and no "auto: <stage>" chip here: the
                         PipelineMap right below this header already draws both
                         — the declared node as the current ring, the detected