[C++] Audit uses of datetime formatting

[asfimport]

The arrow_vendored::date library allows us to write date/time formatting routines relatively easily, but it may throw exceptions or return silently erroneous data (see ARROW-12011). We should audit all our uses or date/time formatting routines from that library and make sure we don't let corner cases slip through.

Reporter: Antoine Pitrou / @pitrou
Watchers: Rok Mihevc / @rok

Related issues:

• [C++][Python] Crashes and incorrect results when converting large integers to dates (is related to)

_{Note: This issue was originally created as ARROW-13738. Please see the migration documentation for further details.}