chat urls: a group is a path, a session decides its own directory

the chat group moves from ?cwd= to a path suffix behind a g/ discriminator
(/chat/g/home/me/project), and a session url carries no group at all.

the real fix is not the spelling. a session's working directory was read back
off the query string to decide where the agent executes, so the address bar was
the authority on where code runs. a pasted or refreshed /chat/<id> arrives with
no ?cwd= at all, so a turn sent before the resolve landed ran in the default
general_chat_sessions dir instead of the project; and a hand-edited ?cwd= could
name a group the session doesn't belong to, with nothing to reconcile them.

loadClaudeSessionById already resolves a session's cwd from the id alone, so the
id is the only source of truth there. it now travels on SelectedSession.cwd,
which is what the composer reads. the url can no longer contradict it.

the vocabulary lives in apps/ChatHistory/chat-routes.ts so a link built in a
panel and one built in a screen cannot drift.

also: startAgentRun no longer returns a literal chatUrl — it returns cwd and
AgentRunnerModal builds the link, so the server holds no copy of the frontend
url shape. and the post-turn permalink strips a stale ?cwd= instead of carrying
it forward onto the new session's url.

walkthrough doc gains item 13.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

src/servers/api/agents/agent-runner.ts

@@ -117,10 +117,14 @@ type StartAgentRunParams = {
 export type StartAgentRunResult = {
   sessionKey: string;
   dirName: string;
+  /**
+   * The directory the run executes in — which is also its project group in /chat, so the caller can
+   * build the link to it. This used to also return a ready-made `chatUrl`, which meant the server held
+   * an opinion about frontend URL shape and drifted the moment that shape changed. `cwd` is the fact;
+   * the URL is the frontend's business (`chatListPath`).
+   */
   cwd: string;
   model: string;
-  /** Where to look at this run: the agent's own project group in /chat, newest session on top. */
-  chatUrl: string;
 };
 
 export async function startAgentRun(params: StartAgentRunParams): Promise<StartAgentRunResult> {
@@ -204,6 +208,5 @@ export async function startAgentRun(params: StartAgentRunParams): Promise<StartA
     dirName: agent.dirName,
     cwd,
     model,
-    chatUrl: `/chat?cwd=${encodeURIComponent(cwd)}`,
   };
 }