This has been covered many times before.
Firstly insurance cover needs to be checked. Most companies will put a 125cc limit on machines rented.
Most rented bikes are between 100 and 160 cc so you need to be careful when renting.
Some companies don't cover motorbikes at all...they are regarded as "extreme" activities.
The idea of SCOOTER is a fallacy there is no such legal term anywhere. The bikes for rent are mostly step-thoughs, but they have 2 wheels and as such are motorbikes.
Thailand does not recognise any 2 wheeled vehicle as anything but a category A motorbike on the IDP under the Vienna treaty.
US has not ratified this treaty. Thailand has in 2020.
Without a valid IDP, insurance may be voided anyway.
To ride a motorcycle in Thailand you need an IDP and a FULL motorcycle licence from home. Any "moped" "scooter" or provisional licence is not sufficient.
Before you leave home, get your IDP and make sure you have category A m/c on it...A1 is no good.
PS insurance in Thailand is unlikely to cover you after 3 months in the country... you need a Thai d/l by then