Gateway: review fixes for stale summaries, history cursors that survive a moving window, timeouts on T3 calls, push size, T3's snooze rules, and input checks

docs/api.md

@@ -103,7 +103,7 @@ directory), the search, the subagent's title or the tool's name, trimmed to abou
 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.
 
-`changes` totals the files the thread's latest run changed. It is null when the run changed no
+`changes` totals the files the thread's latest run changed, counting only edits that ran. It is null when the run changed no
 files, and, like `lastMessage`, until the gateway has read the thread.
 
 ```
@@ -234,7 +234,9 @@ POST /v1/threads/:hostId/:threadId/unsnooze
 ```
 
 Snoozing hides a finished thread from Recent until `until`, which must be in the next 30 days. Then
-it comes back on its own. A snoozed thread that starts working or waiting on you shows as usual.
+it comes back on its own. A snoozed thread that starts working or waiting on you shows as usual,
+and one that fails after it was snoozed comes back to Recent, the same rules T3 uses. A snoozed
+thread that finishes again does not push.
 
 Thread detail fills `request` and `via` the same way as the feed when a subagent waits on you.