QA: verify that light clients recover messages missed while staying online (gap deferred from #7604)

[glitchminer]

#7604 reconciles history after offline periods. A client that stays online never reconciles.

A filter subscription can die while the client stays online. The client only notices at the next
60-second ping (one server-side cause: #7605). Messages pushed during that window are lost, and
nothing re-fetches them.

We confirmed the behaviour on a real device (2026-07-06, Android light client on status.prod):
the app reported "connected" for 36 minutes and only queried the store nodes at login. Messages
missed during the session were never recovered.

This case was left out of #7604 on purpose, to be handled with the other light client fixes
(#7605, #7606). This issue keeps it visible until then. Part of #7568.

QA task

When the light client fixes land, re-run the device check above: kill the filter subscription
while the client stays online, then confirm the missed message is recovered.

Done when

A stays-online light client recovers a message its filter subscription dropped, shown on a real
device or in a functional test.