yes, you can still enter visa-exempt for initial 30 day permission to stay and then extend at immi for another 30 days.
however you will most likely still need insurance for COVID as this has been a mandatory requirement for some time now and is hanging around like a bad smell. but it's a fluid situation so who knows what changes they'll make before your trip.
insurance doesn't need to be from the Thai providers, those policies are considered worthless by the aseannow hive mind ????. but you can use a foreign policy if they'll give you a Travel Certificate confirming that they provide COVID coverage for X dollars. Thailand Pass will accept such a document, or a letter from the insurer, according to other posters.
and yes, Thailand Pass is about to be updated for the 1 May 2022 changes so no point trying to do anything there at the moment.