feat(ai-router): test an endpoint before saving it, and re-point a live lane

Two gaps left by the AI Router feature: a profile could be saved without ever
being reachable, and a lane's router could only be chosen at creation.

**POST /api/ai-routers/test** answers the question saving cannot. It sends one
Anthropic-style message capped at a single output token to `<baseUrl>/v1/messages`
with a 15s timeout — the wire shape a claude lane's eight env keys point at, so
what is tested is what will actually run. A router that answers is a 200 here
whatever it replies: `{ ok, status, message }` carries the router's own words,
and `status` is null when nothing answered at all. 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 — so testing a retyped
endpoint needs a retyped key (`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.

Network failures report `error.cause`, not `error.message`: node's fetch reports
every transport failure as the same useless "fetch failed" and hides the part
the user can act on (ECONNREFUSED, ENOTFOUND, a TLS error) one level down.

**The lane card carries an AI Router select.** The Add-lane modal was the only
place a router was chosen, and a lane outlives its creation. Switching goes
through `POST /api/lanes/:id/router/apply` — never a lane PATCH — because the
DB column and the lane's own config on disk may only move together. A failed
apply puts the select back rather than leaving the card claiming a router the
lane did not get. Hidden when `native` is the only profile: a select with one
option is a control that cannot do anything.

Adds `Lane.router_profile` to the client type (the payload already carried it).

server/lib/ai-routers.js

@@ -21,6 +21,11 @@
  * native" is the same single write path as "switch to a router". It cannot be
  * edited, removed, or shadowed by a saved profile.
  *
+ * `testRouter` is the one thing here that talks to the network: the smallest
+ * real request a claude lane would make, so "saved" and "actually works" stop
+ * being the same claim. It is deliberately NOT a generic proxy — see the note
+ * on its stored-key fallback.
+ *
  * @author Nguyễn Ngọc Trí Vĩ <vinnt@smartgift.vn>
  */
 
@@ -307,12 +312,93 @@ function removeRouter(name) {
   return { removed: name };
 }
 
+/** How long a connection test waits before calling the endpoint dead. */
+const TEST_TIMEOUT_MS = 15_000;
+
+/** Enough of a failing router's own words to be actionable, not enough to flood. */
+const TEST_BODY_MAX = 300;
+
+/**
+ * Probe a router endpoint with the smallest real request a claude lane makes:
+ * one Anthropic-style message capped at a single output token.
+ *
+ * Deliberately the CLAUDE wire shape and not Codex's `responses` one. A profile
+ * is not tool-specific, so a test has to pick; `/v1/messages` is what a claude
+ * lane's eight env keys point at, and it is the path a router has to serve for
+ * this feature to work at all.
+ *
+ * **The stored key is only ever sent to the endpoint it was stored against.**
+ * A blank `apiKey` falls back to the saved profile named by `name` — but only
+ * when the submitted `baseUrl` still matches the saved one. Without that check
+ * this route would be a way to make the server POST a saved API key to any URL
+ * a browser names, which is exactly the leak `listRouters` exists to prevent.
+ *
+ * A router that answers is a success even when it answers with an error: the
+ * outcome is reported (`ok`, `status`, `message`), never thrown. Only bad INPUT
+ * throws.
+ *
+ * @param {{name?:string, baseUrl:string, apiKey?:string, model:string}} input
+ * @returns {Promise<{ok:boolean, status:number|null, message:string}>}
+ */
+async function testRouter(input = {}) {
+  const baseUrl = normalizeBaseUrl(input.baseUrl);
+  const model = normalizeModel(input.model);
+
+  let apiKey = typeof input.apiKey === "string" ? input.apiKey.trim() : "";
+  if (!apiKey && input.name) {
+    const stored = readRouter(input.name);
+    if (stored && normalizeBaseUrl(stored.baseUrl || "") === baseUrl) apiKey = stored.apiKey || "";
+  }
+  if (!apiKey) throw err("EBADKEY", "enter the API key to test this endpoint");
+
+  let res;
+  try {
+    res = await fetch(`${baseUrl}/v1/messages`, {
+      method: "POST",
+      headers: {
+        "content-type": "application/json",
+        // Both, because routers disagree on which one they read, and it is the
+        // same key going to the same endpoint either way.
+        "x-api-key": apiKey,
+        authorization: `Bearer ${apiKey}`,
+        "anthropic-version": "2023-06-01",
+      },
+      body: JSON.stringify({
+        model,
+        max_tokens: 1,
+        messages: [{ role: "user", content: "ping" }],
+      }),
+      signal: AbortSignal.timeout(TEST_TIMEOUT_MS),
+    });
+  } catch (e) {
+    // Unreachable, DNS failure, TLS refusal, timeout — a real answer about the
+    // endpoint, so it is a result and not a 500.
+    //
+    // `cause` first: node's fetch reports every transport failure as the same
+    // useless "fetch failed", and hides the part the user can act on
+    // (ECONNREFUSED, ENOTFOUND, a TLS error) one level down.
+    return {
+      ok: false,
+      status: null,
+      message: e.name === "TimeoutError" ? "timed out" : (e.cause && e.cause.message) || e.message,
+    };
+  }
+
+  const body = await res.text().catch(() => "");
+  return {
+    ok: res.ok,
+    status: res.status,
+    message: res.ok ? model : body.slice(0, TEST_BODY_MAX) || res.statusText,
+  };
+}
+
 module.exports = {
   listRouters,
   getRouter,
   createRouter,
   updateRouter,
   removeRouter,
+  testRouter,
   MODEL_SLOTS,
   BUILTIN_NAME,
   NATIVE,