I'm moving again in a few weeks and I'm not concerned at all. I also moved to a brand new state on April 1st. That was a really weird few weeks for sure but it's fine now. Masks are everywhere, virtual tours or self-show only.
Obviously not factoring in that you don't WANT to move here just saying that if you're worried about the process it will probably be fine apart from possibly having to decide on a place via a Skype tour.
Entering your home without your consent is definitely illegal. You might be able to use the threat of suing over that alone as something to get your landlord to renew your lease (e.g. have a lawyer write a letter about them entering your home without your consent, and offering lease renewal as the "settlement"/alternative to going to court over it.)
Did your annual lease end and you were leasing monthly?