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.

docs/LANES.md

@@ -188,7 +188,7 @@ Every destructive `POST /api/lanes/:id/:action` must echo back an `expect` objec
 ### Environment variables
 
 - **`LANES_ROOT`** (default `~/.claude/agenthub-lanes`) — the directory managed worktrees are provisioned under; also the boundary that safety check 2 resolves paths against.
-- **`LANE_DEAD_SEC`** (default `300`) — seconds of silence before a lane whose stage matches `/watch|poll/i` flips from `active` to `dead` liveness.
+- **`LANE_DEAD_SEC`** (default `300`) — seconds of silence before a lane whose stage matches `/watch|poll/i` (or whose status is `running`) flips from `active` to `dead` liveness. Silence is counted from the newer of the lane session's last event and the start of the lane's current run (`dashboard_runs.started_at`), so a run started a moment ago is never judged by the previous session's quiet. A lane no hook ever binds a session to (a catalog tool, Codex without its hooks) has no silence to measure and stays `active`.
 - **`LANE_BASE_BRANCH`** (default `main`) — the base branch a new managed worktree resolves against when a request omits `base`. An explicit `--base <branch>` (or request body `base`) always wins over this default.
 - **`LANE_BRANCH_PREFIX`** (default `feat/`) — the prefix used to build a new managed worktree's feature branch name (`<prefix><slug>`).
 
@@ -1703,7 +1703,7 @@ agenthub stage <stage> [--evidence "..."]         # Report the current stage
 
 ## Lanes on any AI tool
 
-A lane can run any AI coding CLI in the AI Tools catalog (`server/data/ai-tools/*.json`, plus any `*.json` in `DASHBOARD_AI_TOOLS_DIR`, which replaces a built-in file with the same `id` but may not set `launcher`). The **AI Tools** button at the right of the Settings tab bar opens a dialog (also `/settings#ai-tools`) that lists what is installed (found on PATH; **Refresh** re-reads the login shell's PATH first) with an enable switch, **Set default** and **Update** (for every tool whose catalog file names an updater — no version lookup, the updater itself reports "up to date"), and, folded behind a disclosure, what is available to install with a homepage link. The Add-lane modal shows the chosen tool as one button (the default until changed); clicking it lists every installed, enabled tool as buttons to pick from; `agenthub lanes add --tool <id>` does the same from a terminal.
+A lane can run any AI coding CLI in the AI Tools catalog (`server/data/ai-tools/*.json`, plus any `*.json` in `DASHBOARD_AI_TOOLS_DIR`, which replaces a built-in file with the same `id` but may not set `launcher`). The **AI Tools** button at the right of the Settings tab bar opens a dialog (also `/settings#ai-tools`) that lists what is installed (found on PATH; **Refresh** re-reads the login shell's PATH first) with an enable switch, **Set default** and **Update** (for every tool whose catalog file names an updater — no version lookup, the updater itself reports "up to date"), and, folded behind a disclosure, what is available to install with a homepage link. The Add-lane modal shows the chosen tool as one button (the default until changed); clicking it lists every installed, enabled tool as buttons to pick from; `agenthub lanes add --tool <id>` does the same from a terminal. The run form's **Model** picker lists the lane tool's own models (`GET /api/ai-tools/:id/models`; Claude, Codex, and any catalog tool whose file declares `model: { flag }` — the id is validated and passed as `<flag> <id>`), plus **Custom…**, and starts on the tool's default model when one is set.
 
 A catalog file:
 
@@ -1714,9 +1714,11 @@ A catalog file:
   "detect": ["agy"],
   "homepageUrl": "https://antigravity.google/docs/cli/overview",
   "prompt": { "mode": "flag", "flag": "-i" },
+  "model": { "flag": "--model", "vendor": "google" },
+  "config": [{ "path": "~/.gemini/GEMINI.md" }],
   "resume": ["--continue"],
   "bypass": ["--dangerously-skip-permissions"]
 }
 ```
 
-`detect` lists bare command names (the first found on PATH is what runs), `requires` other commands that must be present, `args` fixed leading args, `prompt.mode` one of `argv` (optional `separator: "--"`), `flag` (`flag`), or `after-start` (`delayMs`, default 3000 — the prompt is pasted into the pane once the CLI is up). `resume` enables **Resume last session**; `bypass`/`bypassEnv` enable the run form's per-run **Bypass permissions** switch, which is off every time the form opens. Every non-Claude lane has no pipeline, no agents install and no AI Router (native only, except Codex); running/idle comes from the exited-pane heal sweep.
+`detect` lists bare command names (the first found on PATH is what runs), `requires` other commands that must be present, `args` fixed leading args, `prompt.mode` one of `argv` (optional `separator: "--"`), `flag` (`flag`), or `after-start` (`delayMs`, default 3000 — the prompt is pasted into the pane once the CLI is up). `model.flag` (optional `vendor`: `claude`/`openai`/`google`, whose priced models the picker offers) puts the run form's model before the prompt; `config` (built-in and release files only, like `install`) lists the `~/`-relative files the tool's Settings tab may edit — `format` `json`/`jsonc`/`text`, guessed from the extension, and never a credential-looking name; `resume` enables **Resume last session**; `bypass`/`bypassEnv` enable the run form's per-run **Bypass permissions** switch, which is off every time the form opens. Every non-Claude lane has no pipeline, no agents install and no AI Router (native only, except Codex); running/idle comes from the exited-pane heal sweep.