How can I join a university class conducted online as a non-matriculating student during COVID-19?
What types of schools will allow non-matriculated participation?

I'll skip this part, because honestly it was news to me that there are universities that don't do this.  Usually the emphasis is on job-related courses.

What is the application process like?

Very simple, if you can pay.  They want your money.

How do I find these?

Look for a &quot;school of continuing education,&quot; &quot;university extension&quot; or similar.  If you do not want something job-related, you might look at programs marketed to retirees.  In some places, such as those with a shortage of classrooms during teaching periods, this may be easier if you look for summer courses.  Availability of classrooms is not, of course, relevant for online courses.