While you can use your house book as proof of address it definitely isn't required. You only need a certificate of residence from immigration. Not even a license is required to buy a bike from a dealer.
I did this recently. Don't use FedEx or UPS or any of the big ones, use USPS. Also declare the package as used items, declare a value of under $20 and put in a thai friends name if possible. I did this and my package was delivered straight to my door with zero taxes of any kind. Also Thailand post and USPS work together so your tracking number will work on both the thai post website and the USPS website. You'll get more accurate tracking when you track it on the USPS site when in the states and then switching to the thai post site once it gets to Thailand.
Go to blue tree immigration if you are close for the certificate of residence as they mentioned when they opened they will have signs up with prices for services to avoid any "mistakes" happening like someone who had been recently charged for a certificate of residence at Phuket town immigration lol.
You need a certificate of residence or house registration book. Pay a small fee(305 for car license in Chiang mai) to have your license converted to a thai license. Quick eye test as well. I don't know if you need the medical certificate or not when you are just converting a license but I would get 1 to be sure.
I've already done 3 covid extensions. But the first was when they were just letting you do 1 additional extension on top of the regular extension and was only for 30 days so it's a bit of a grey area.