feat(ai-proxy): Update 9router button — shut down, npm update, relaunch hidden

Settings → AI Proxy gains an admin-only Update 9router button beside
Config 9router. One in-memory job (server/lib/nine-router-update.js) stops
9router (its user unit, else this account's own 9router processes), runs
npm install -g --prefix <its prefix> 9router@latest (sudo -n only when
sudoers already allows it, probed before anything stops), then relaunches
it hidden only if it was running. A failed update still relaunches the old
version. Nothing in the request names a command, path or package.

docs/API.md

@@ -3033,6 +3033,8 @@ The login profiles of the AI tools other than Claude Code (`server/lib/tool-prof
 ```
 GET    /api/ai-proxies                Every saved profile, the built-in `native` one first
 GET    /api/ai-proxies/9router        `{ installed }` — is a `9router` binary on the server's PATH (nothing is run)
+GET    /api/ai-proxies/9router/update versions, running state, `blocker`, current job (`?fresh=1` re-asks npm)
+POST   /api/ai-proxies/9router/update shut down → npm update → start hidden; 202 + job (admin)
 POST   /api/ai-proxies                Create — Body: { label, baseUrl, apiKey?, model, models?, behavesAs?, scope? }
 POST   /api/ai-proxies/test           Probe an endpoint — Body: { baseUrl, model, apiKey?, name? }
 PATCH  /api/ai-proxies/:name          Update the same fields, all optional
@@ -3055,6 +3057,11 @@ A **proxy profile** is an endpoint that stands in front of Claude Code or Codex
 
 **`GET /api/ai-proxies/9router`** answers `{ installed: boolean }` from a PATH lookup only (the server's and the login shell's PATH); the AI Proxy page shows a **Config 9router** link beside **Add profile**, opening 9router's own UI in a new tab on the dashboard's own host, port 20128 (`http://<the host the page was opened on>:20128` — e.g. `http://10.1.13.7:20128` from a LAN browser, so the viewer needs no 9router of their own; 9router must listen beyond loopback for that), only when it is `true`.
 
+**Update 9router** (`server/lib/nine-router-update.js`; the AI Proxy page's button beside Config 9router, an admin's only — `/ai-proxies/9router` and `/ai-routers/9router` are in `ADMIN_WRITE_PREFIXES`). `GET /api/ai-proxies/9router/update` answers `{ installed, version, latest, updateAvailable, running, managedBy: "systemd"|"process"|null, blocker: {code, message, command?}|null, job }`. `POST` starts one job (202; `EBUSY` while one runs, else 409 with the blocker's code — checked BEFORE anything is stopped) of three steps, each `pending|running|done|failed|skipped`:
+1. **shutdown** — a running `9router.service` user unit is `systemctl --user stop`ped; otherwise this account's processes whose argv names the install's `cli.js` get SIGTERM, then they and their descendants SIGKILL after 5 s; the step waits until the port is free. Skipped when nothing ran.
+2. **update** — `npm install -g --prefix <the install's own prefix> --prefer-online 9router@latest`; a prefix this account cannot write runs it under `sudo -n`, only when `sudo -n <npm> --version` succeeds (else `ENOPERM` with `command: "sudo npm install -g 9router@latest"`).
+3. **relaunch** — only when 9router was running before: `systemctl --user start 9router.service`, or `node cli.js --tray --no-browser --skip-update -p <old port> [-H <old host>]` detached in its own `systemd-run --user --scope` (plain detached spawn without one); done once the port answers. Runs even after a failed update.
+
 **`POST /api/ai-proxies/test`** answers the question saving cannot: does this endpoint, with this key, actually serve this model — for each CLI? It sends, in parallel and with a 15 s timeout each, one Anthropic-style message capped at a single output token to `<baseUrl>/v1/messages` (what Claude Code calls) and one OpenAI Responses call (`max_output_tokens: 16`) to `<baseUrl>/v1/responses` (what Codex calls). A proxy that answers is a `200` here whatever it replies: `{ claude: { ok, status, message }, codex: { ok, status, message } }`, each carrying the proxy's own words (truncated to 300 characters), `status` `null` when nothing answered at all. A proxy that serves only one wire shape shows one green line and one red. Only bad input is a 4xx.
 
 The stored key is only ever sent to the endpoint it was stored against. A blank `apiKey` falls back to the key of the profile named by `name`, but **only** while the submitted `baseUrl` still equals the saved one (both compared without `/v1`) — so testing a retyped endpoint needs a retyped key (`400 EBADKEY`). Without that rule this route would be a way to make the server POST a saved API key to any URL a browser names.