debuggerd_client: also log errors to the dump file.

Dumping stack in ANR can fail, but error message is only printed
to logcat. To allow easier debugging of such cases we add the
error messages in the ANR file as well.

Also factor out some duplication, inline single-call functions to
their call sites, and make some of the lambdas clearer by only having
implicit state unrelated to their primary purpose in captures but
passing as arguments things they fundamentally need to do their job
(and actually adding some duplication for time_left() which was subtle
enough to fool me into thinking that we only needed one call of
set_timeout(), which I've renamed to update_timeout()).

Bug: 191172191
Test: Manual
Change-Id: I39a50ca5b72059bfeff48b010d3be44f19eb32fa