job change and health insurance change - HSA and FSA in the same year?

I recently changed jobs in August 2020.  I previously had an HDHP health insurance plan with HSA, and I want to know if I can switch health insurance to a non-HDHP and contribute to a standard FSA for the remainder of the year.  I'm looking at IRS Pub 969 and having trouble finding any information on this scenario, particularly whether there are potential tax penalties.  Thank you.