I am in a similar situation as Elena is, arrived in early march on TR visa, already extended 30 days which are due 3rd of June, went to Chang Wattana yesterday to get first 60 day covid extension. The answer was they would start counting 60 days from the day i apply (yesterday) so i said, ok then i will come next week. They gave me additional papers to fill at home.
I came to Bangkok on 6th of March on TR visa, two days ago i went to Immigration Bureau to extend 30 days and havent been asked for TM30. If i apply for covid extension later on, I am pretty sure they would ask for.