Most countries passport can arrive on 30 day free Exemption stamp or on 60 day Tourist Visa (sticker already in passport or online application now also possible)
Both can extend at local immigration for 30 days.
After if still applicable one might be eligible for the 60day COVID extension. But for now only till Jan 25,
Check into whatever hotel-guesthouse. Demand they register you within 24hrs.(they have to by law). During your time staying at that address apply for your extension.
Note that Chiang Mai is known for giving 15 days "under consideration" stamps, so you have to go back to get the rest (and still be registered in Chiang Mai district, not Pai for example, which is different district).
They also asking more paperwork than KP in the form of maybe onward flights, Embassy letters, etc . All this has been reported over the last 2 weeks to be the case for some.
As far as my knowledge goes. 1st C-extension stamped from day of application. 2nd and onwards from expiry date of current stamp. This been observed allover the country over the past year.