As of right now, we have at least two people posting to debian-user
about DNS failures involving what appears to be their home router's
forwarding DNS service, and Debian 10.9.
Switching the nameserver lines in resolv.conf to something *other than*
the home router's DNS seems like a reasonable workaround. Many of us
do that full-time anyway.
If anyone knows of a change to libc6 or libnss* in Debian 10.9 that might
be the underlying cause of these issues, please file a bug report or
something so it can be fixed.
Then I would
sudo chattr +i /etc/resolv.conf
That's *one* of the methods listed on the wiki. Just be aware that it
can leave a whole bunch of /etc/resolv.conf.dhclient-new.* files sitting
around, and be prepared to remove them.
(I use a weekly crontab job.)