Gateway: activity line, thread history paging, a project's threads, and a thread's subagents

docs/api.md

@@ -77,6 +77,7 @@ FeedItem {
   "phase": "waiting_for_approval",
   "updatedAt": "2026-11-01T09:41:00.000Z",
   "lastMessage": "Parser and tests are written. I want to run the suite.",
+  "activity": { "kind": "command", "text": "bun test", "startedAt": "..." } | null,
   "request": PendingRequest | null,
   "via": { "hostId": "...", "threadId": "...", "title": "Check Panama PATH" } | null
 }
@@ -92,6 +93,12 @@ when the gateway cannot find its parent, or the parent already shows a request.
 `failed`. `lastMessage` is the agent's latest message trimmed to about 280 characters. It can be null
 for a moment after a thread changes.
 
+`activity` is the newest step the agent has in progress. `kind` is `command`, `edit`, `search`,
+`web`, `subagent`, `thinking` or `tool`, and `text` is the command line, the file name (without its
+directory), the search, the subagent's title or the tool's name, trimmed to about 80 characters.
+Monitors are left out, since they run for hours. It is null when no step is in progress. The gateway
+rereads a running thread at most every 5 seconds, so it can lag that much.
+
 ```
 PendingRequest {
   "id": "...",
@@ -112,11 +119,25 @@ thread". For questions (`kind: "user_input"`), `options` is empty and `questions
 ```
 GET /v1/threads/:hostId/:threadId
 
-200 { "item": FeedItem, "messages": [Message], "canStop": true, "askFirst": false }
+200 { "item": FeedItem, "messages": [Message], "canStop": true, "askFirst": false,
+      "earlierCursor": "w12" | null, "subagents": [ThreadRow] }
+ThreadRow { "hostId": "...", "threadId": "...", "title": "Check PATH", "phase": "running" | null,
+            "settled": false, "updatedAt": "..." }
 Message { "id": "...", "role": "assistant", "text": "...", "createdAt": "..." }
 ```
 
-`messages` holds the last 20, oldest first, each trimmed to 2000 characters.
+`messages` holds the last 20, oldest first, each trimmed to 2000 characters. `subagents` lists the
+threads this one started, its own subagents and `delegate_task` children on any host, newest first.
+A ThreadRow's `phase` is null for a thread that never ran or was stopped.
+
+```
+GET /v1/threads/:hostId/:threadId/history?cursor=<earlierCursor>
+
+200 { "messages": [Message], "earlierCursor": "..." | null }
+```
+
+The 20 messages before the ones the watch has, oldest first. Pass the returned `earlierCursor` for
+the page before that. It is null at the start of the thread. Cursors are opaque.
 
 ```
 POST /v1/threads/:hostId/:threadId/messages
@@ -192,6 +213,17 @@ GET /v1/summary
 
 `next` is the thread that has waited longest for you, or null.
 
+## Browse
+
+```
+GET /v1/projects/:hostId/:projectId/threads
+
+200 { "items": [ThreadRow] }
+```
+
+A project's newest 50 threads, settled ones included, newest first. Subagents are left out and
+listed under their parents instead. Hosts and projects come from `GET /v1/projects`.
+
 ## New thread
 
 ```