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/index.js

@@ -548,6 +548,21 @@ function startBackgroundServices() {
     }, HEAL_MS);
     if (healTimer.unref) healTimer.unref();
   }
+  // Another dashboard on the same database (hooks reach only one of them)
+  // moving a lane: re-broadcast it here. One pragma per beat when nothing
+  // changed. Off with DASHBOARD_LANE_SYNC_MS=0.
+  const LANE_SYNC_MS = Number(process.env.DASHBOARD_LANE_SYNC_MS ?? 2_000);
+  if (Number.isFinite(LANE_SYNC_MS) && LANE_SYNC_MS > 0) {
+    const { broadcastForeignLaneChanges } = require("./routes/lanes");
+    const laneSyncTimer = setInterval(() => {
+      try {
+        broadcastForeignLaneChanges();
+      } catch (err) {
+        console.warn("lane sync failed:", err.message);
+      }
+    }, LANE_SYNC_MS);
+    if (laneSyncTimer.unref) laneSyncTimer.unref();
+  }
   // Continuous discovery of sessions under ~/.claude/projects. The one-time
   // legacy backfill above runs only once (marker-gated), so a project added
   // later whose sessions never flow through hooks would otherwise stay invisible