[lldb-dap] Fix a race during shutdown (#91591)

lldb-dap was setting a flag which was meant to shut it down as soon as
it sent a terminated event. The problem with this flag is two-fold:
- as far as I can tell (definitely not an expert here), there's no
justification for this in the protocol spec. The only way I found to
shut the server down was to send it a disconnect request.
- the flag did not actually work most of the time, because it's only
checked between requests so nothing will happen if the server starts
listening for a new request before a different thread manages to send
the terminated event. And since the next request is usually the
disconnect request, everything will operate normally.

The combination of these two things meant that the issue was largely
unnoticable, except for rare flaky test failures, which happened when
the handler thread was too slow, and checked the flag after it has
already been said. This caused the test suite to complain as it did not
get a response to th...