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/__tests__/__snapshots__/screens.snapshot.test.tsx.snap

@@ -6996,6 +6996,47 @@ exports[`screen snapshots > Settings 1`] = `
           </svg>
           Appearance
         </button>
+        <button
+          class="inline-flex items-center gap-1.5 text-xs whitespace-nowrap px-2.5 py-1.5 rounded-lg border transition-colors flex-shrink-0 border-border text-fg-secondary hover:text-fg-primary hover:bg-surface-3"
+          type="button"
+        >
+          <svg
+            class="lucide lucide-bot w-3.5 h-3.5"
+            fill="none"
+            height="24"
+            stroke="currentColor"
+            stroke-linecap="round"
+            stroke-linejoin="round"
+            stroke-width="2"
+            viewBox="0 0 24 24"
+            width="24"
+            xmlns="http://www.w3.org/2000/svg"
+          >
+            <path
+              d="M12 8V4H8"
+            />
+            <rect
+              height="12"
+              rx="2"
+              width="16"
+              x="4"
+              y="8"
+            />
+            <path
+              d="M2 14h2"
+            />
+            <path
+              d="M20 14h2"
+            />
+            <path
+              d="M15 13v2"
+            />
+            <path
+              d="M9 13v2"
+            />
+          </svg>
+          AI Tools
+        </button>
         <button
           class="inline-flex items-center gap-1.5 text-xs whitespace-nowrap px-2.5 py-1.5 rounded-lg border transition-colors flex-shrink-0 bg-accent/15 border-accent/30 text-accent"
           type="button"
@@ -8089,6 +8130,105 @@ exports[`screen snapshots > Settings 1`] = `
         </div>
       </div>
     </section>
+    <section
+      class="scroll-mt-24"
+      id="ai-tools"
+    >
+      <h3
+        class="text-sm font-medium text-fg-secondary flex items-center gap-2 mb-1"
+      >
+        <svg
+          class="lucide lucide-bot w-4 h-4 text-fg-muted"
+          fill="none"
+          height="24"
+          stroke="currentColor"
+          stroke-linecap="round"
+          stroke-linejoin="round"
+          stroke-width="2"
+          viewBox="0 0 24 24"
+          width="24"
+          xmlns="http://www.w3.org/2000/svg"
+        >
+          <path
+            d="M12 8V4H8"
+          />
+          <rect
+            height="12"
+            rx="2"
+            width="16"
+            x="4"
+            y="8"
+          />
+          <path
+            d="M2 14h2"
+          />
+          <path
+            d="M20 14h2"
+          />
+          <path
+            d="M15 13v2"
+          />
+          <path
+            d="M9 13v2"
+          />
+        </svg>
+        AI Tools
+      </h3>
+      <p
+        class="text-xs text-fg-muted mb-4"
+      >
+        AI coding CLIs AgentHub can run in a lane. Detected on this machine's PATH; a disabled tool is hidden from Add lane.
+      </p>
+      <div
+        class="card p-5 space-y-5"
+      >
+        <div>
+          <div
+            class="flex items-center justify-between gap-3 mb-2"
+          >
+            <p
+              class="text-xs font-medium text-fg-secondary"
+            >
+              Installed (0 detected)
+            </p>
+            <button
+              class="inline-flex items-center gap-1.5 rounded-md border border-border px-2 py-1 text-xs text-fg-secondary hover:bg-surface-3 disabled:opacity-50"
+              type="button"
+            >
+              <svg
+                class="lucide lucide-refresh-cw w-3.5 h-3.5"
+                fill="none"
+                height="24"
+                stroke="currentColor"
+                stroke-linecap="round"
+                stroke-linejoin="round"
+                stroke-width="2"
+                viewBox="0 0 24 24"
+                width="24"
+                xmlns="http://www.w3.org/2000/svg"
+              >
+                <path
+                  d="M3 12a9 9 0 0 1 9-9 9.75 9.75 0 0 1 6.74 2.74L21 8"
+                />
+                <path
+                  d="M21 3v5h-5"
+                />
+                <path
+                  d="M21 12a9 9 0 0 1-9 9 9.75 9.75 0 0 1-6.74-2.74L3 16"
+                />
+                <path
+                  d="M8 16H3v5"
+                />
+              </svg>
+              Refresh
+            </button>
+          </div>
+          <ul
+            class="divide-y divide-border rounded-md border border-border"
+          />
+        </div>
+      </div>
+    </section>
     <section
       class="scroll-mt-24"
       id="pricing"