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).

client/src/i18n/locales/en/lanes.json

@@ -142,5 +142,7 @@
   "addLaneRouterHint": "Native talks to the vendor's own API. An AI Router profile is written into this lane's own config when it is created.",
   "addLaneRouterEmptyHint": "No router profile saved yet — add one under Settings › AI Router.",
   "addLaneSetupRouter": "Model endpoint",
-  "addLaneRouterLoading": "Loading router profiles…"
+  "addLaneRouterLoading": "Loading router profiles…",
+  "router.label": "AI Router",
+  "router.applied": "Applied. A session already running in this lane keeps the old one until it restarts."
 }