auth: strip prompt=consent from initial authorize (auto-approve for connector)

Claude forces the consent screen with prompt=consent; the consent endpoint's
signed-query round-trip is brittle. Simpler: drop prompt=consent from the initial
unsigned authorize so skipConsent applies and no consent page is shown. Also pass
raw query bytes to the login/consent handlers.

src/server.ts

@@ -77,6 +77,11 @@ async function handleConsent(req: IncomingMessage, res: ServerResponse, rawSearc
 
 const server = createServer((req, res) => {
   const url = new URL(req.url ?? "/", "http://localhost");
+  // Raw query bytes (the URL API re-encodes .search, which breaks Better Auth's
+  // signed oauth_query check on /consent). Take the query straight from req.url.
+  const rawUrl = req.url ?? "/";
+  const qIndex = rawUrl.indexOf("?");
+  const rawSearch = qIndex >= 0 ? rawUrl.slice(qIndex) : "";
   if (url.pathname !== "/healthz") {
     // Request-level trace (path only, no query — avoids logging codes/tokens).
     // eslint-disable-next-line no-console
@@ -89,13 +94,25 @@ const server = createServer((req, res) => {
     return;
   }
   if (url.pathname === "/login" && req.method === "GET") {
-    void startLogin(req, res, url.search);
+    void startLogin(req, res, rawSearch);
     return;
   }
   if (url.pathname === "/consent" && req.method === "GET") {
-    void handleConsent(req, res, url.search);
+    void handleConsent(req, res, rawSearch);
     return;
   }
+  // Claude sends prompt=consent on the initial authorize, which forces the
+  // consent screen even with skipConsent. For a personal connector the login is
+  // the authorization, so strip it from the initial (unsigned) request — the
+  // signed resume after login has a `sig` and is left untouched.
+  if (
+    url.pathname === "/api/auth/oauth2/authorize" &&
+    !url.searchParams.has("sig") &&
+    url.searchParams.get("prompt") === "consent"
+  ) {
+    url.searchParams.delete("prompt");
+    req.url = url.pathname + (url.searchParams.toString() ? `?${url.searchParams}` : "");
+  }
   // Everything else -> Better Auth (async handler).
   void handler(req, res);
 });