Start no AS, peer or peering write after the stop deadline (closes #189)

A write can run past the stop deadline while a full batch's wake-up or a
tick waits beside Stop's context. The select picked one at random, so about
half the time the AS, peer or peering handler started another write after
the deadline. Each loop now takes a waiting stop first, as the prefix
handler's does. The prefix, AS and peer handlers' flush loops were
near-copies, so they are now one function, flushLoop. A new test for each
handler fails about half its runs on the old code.

The AS and peer handler tests give the flush timer an interval longer than
the test. A timer flush during the fill can no longer hang
TestPeerHandlerWaitsAtTheMaximumBatchSize.

Model: opus-5-5

TODO.md

@@ -33,6 +33,11 @@ tested.
 
 # Completed Steps
 
+- 2026-10-27: once the stop deadline has passed, the AS, peer and peering
+  handlers start no write either. A full batch or a tick of the timer that
+  waited while a write ran past the deadline could still start one. The flush
+  goroutines of the prefix, AS and peer handlers now run the same code (closes
+  #189)
 - 2026-10-27: once the stop deadline has passed, the prefix handler starts no
   flush. A batch that filled while a write ran past the deadline could still be
   written after it (closes #188)