Why is the landlord or property manager playing these games?
Or is this just a hypothetical question.
If you are issued a termination notice, then you have to act on it. In other words, take it as being true and look for a new place.
Not withstanding what follow up email the landlord sends, he may never sign a new contract with you, and so the eviction notice stands.
As for the landlord, he does not diminish his rights and can reasonably sign a new contract with you, between the issue of the eviction notice and the end of the contract. He doesn’t need to withdraw the eviction notice because it pertains to the previous contract and not the new one you sign.
The saving grace for you is that if you overstay your lease, the landlord has to get a court order to evict you. You’ll lose but you have some time to find a new place.
Having been a landlord, I fail to understand why a landlord would not want to keep a good tenant, particularly in these times.
Perhaps there is some other reason for him being difficult .