feat: model lists and prices that follow each AI tool, a Settings tab per tool, live lane status (#40)

Pricing: the LiteLLM sync now adds every current Claude / GPT (>= 5) /
Gemini (>= 3) chat model before it is used and keeps its own rows
(model_pricing.source = 'sync', the Auto badge) at the published rate. A
user's row (any PUT) and a deleted pattern (model_pricing_dismissed) are
never touched; a deleted built-in row is not re-seeded at the next start; a
reset re-applies the list at once; retired Claude models are priced only
once used.

Models: GET /api/ai-tools/:id/models reads each tool's own list (Codex's
models_cache.json, Claude's aliases named after the newest version plus
priced versions, a catalog tool's vendor rows plus the models its sessions
used). A catalog `model: {flag, vendor?}` field passes `<flag> <id>`
(validated: never a flag or shell text); a per-tool default model starts
each run, and a resume keeps the session's own model.

Settings: every installed, enabled catalog tool without its own tab gets
one (AiToolConfig.tsx): path, homepage, Update, sessions/cost/lanes,
default model, vendor pricing, and the config files its release catalog
lists, edited over the opened sha, syntax-checked, backed up, written
atomically; credential-looking names refused. Antigravity keeps its hooks
card there.

Lanes: a just-started run no longer reads "dead" (age counts the run's
start while the old session is still bound); a second dashboard on the
same database re-broadcasts the lanes the other changed (PRAGMA
data_version, every 2 s); a lane start with a bad model answers 400.

DB: every migration runs under a cross-process lock (<db>-migrate.lock), so
two dashboards started at once on a fresh database both come up.

server/__tests__/pty-run.test.js

@@ -439,7 +439,7 @@ describe("pty-run", () => {
       return i < 0 ? undefined : call[i].slice(key.length + 1);
     };
 
-    it("starts antigravity by absolute path, dropping flags it has no use for", () => {
+    it("starts antigravity by absolute path, with its model flag and none it has no use for", () => {
       const call = captureNewSession(() =>
         pty.spawnRun({
           laneId: 13,
@@ -451,7 +451,7 @@ describe("pty-run", () => {
           initialPrompt: "hello",
         })
       );
-      assert.deepEqual(paneArgv(call), [at("agy"), "-i", "hello"]);
+      assert.deepEqual(paneArgv(call), [at("agy"), "--model", "opus", "-i", "hello"]);
       assert.equal(envOf(call, "PATH"), process.env.PATH);
 
       tmux.__reset();
@@ -467,6 +467,16 @@ describe("pty-run", () => {
       assert.deepEqual(paneArgv(last), [at("agy"), "--continue", "--dangerously-skip-permissions"]);
     });
 
+    it("refuses a flag-shaped model id for any tool, before tmux is asked", () => {
+      for (const tool of ["claude", "codex", "antigravity"]) {
+        assert.throws(
+          () => pty.spawnRun({ laneId: 16, cwd: "/tmp/repo", tool, model: "--yolo" }),
+          { code: "EBADMODEL" },
+          tool
+        );
+      }
+    });
+
     it("builds each prompt mode, with fixed args first", () => {
       const argvFor = (tool, extra = {}) =>
         paneArgv(