A good battery, once properly charged should hold 12.6 volts, not 12.
If the alternator is charging properly, mine is closer to 14 volts,
not 13.5. 13.5 volts will work, but not optimum.

I am curious if you replaced the battery and alternator at the exact
same time. I have seen many times that a bad battery burn out a new
good alternator in just a few hours or days.

I know it is a PITA, but maybe you need to have your alternator bench
tested in a machine to check the output to see if it can handle the
load.

Another thing to check: The charging wire that connects the alternator
to the battery wire on the starter. Maybe it has a bad connection or
corroded fuse link. That wire had a recall on it when my car was just
a year old. The old wire didn't have a fuse link, the new one did. But
they go bad as well, even intermittent.

James