Await all UI events after each key press in mouse-during-insert test

This test doesn't care about testing things like "if I send the next
key before we have finished reacting to the previous ones, nothing
bad ever happens".

Hence we can until exhaustion after each input.  This should fix
bespoke flakiness. The handling of "c<esc>" should be atomic.

This reasoning probably applies to most tests; waiting for all events
seems like the safest and easiest approach overall (compared to sleep
or sleep-until). The downside is that the tests need changes when
UI code changes but it rarely does, and if it does we can automate
the updates.

Closes #5073

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