One small note -- what got you an interview before 2020 will often not get you an interview now. The market (as you obviously know) is much tougher. The last two managerial roles I've opened have gotten literally thousands of applications within the first week and it's harder to stand out. If you've done a few rounds already, there's probably not much incremental value, though.

Absolutely ask for referrals. You gotta painfully get on LinkedIn for maximum effectiveness -- if you're looking at a company and an ex-coworker you got along with knows someone there, ask for the introduction. It feels awkward and weird but it increases your chances somewhat.