My archive pages and single page custom post types no longer appear on preview/frontend and I get "This page doesn't seem to exist.
It looks like the link pointing here was faulty. Maybe try searching?".
The only thing that I can think of that possibly created the issue was that my WordPress was automatically upgraded to 5.7.2
Could we get access to your site to check what's going on?
Before that I would just try re-saving your permalinks (from Dashboard go to Settings > Permalinks), otherwise please share details.
I will mark your next reply as private so that we can get log-in credentials from you—you may want to create a temporary admin user for us to use that you can later delete. And be sure to have a current backup of your site.
Does this affect archives and single posts of all custom post types?
