fix(ui-chat): fold next-message work details on one frame clock

Folding on the next message reserved the whole closing height as bottom
room and kept scrollTop whenever the input had no transcript echo on this
page: a message from another tab, a queued message delivered after the
previous Turn, or a send from a subagent child in the right Sidebar. A
reader below the fold was left on an empty viewport.

Every batch of closing rows now runs on the viewport's frame-clock driver.
It lands at the tail for this client's own input or a following reader and
otherwise keeps the reader's content still, installing only the room the
landing lacks. Subagent child sends register a local echo and pass its
request id to subagents.prompt, so the child's recorded message retires it.

tsconfig.host.json

@@ -10,6 +10,7 @@
   "include": [
     "apps/web/tests/collapse-timing.e2e.ts",
     "apps/web/tests/notice-wake-tail.e2e.ts",
+    "apps/web/tests/fold-blank-matrix.e2e.ts",
     "apps/web/tests/chat-flow-layout.e2e.ts",
     "apps/web/product-isolation.ts",
     "apps/web/katex-fonts.ts",