I've never seen 135cc scooters in Thailand. Most low-end scooters available for rent are 125cc (Honda Click, Scoopy etc.). The higher category is 155/160cc (Honda PCX, Yamaha Aerox, NMax etc.).
I had the same problem at Ban Laem in November 2022. Was doing my first border hop after 2+ years in Thailand on covid extensions (the whole covid period, including the amnesty). They told me I cannot leave by land because "I was in Thailand too much". The issue was solved by contacting the superintendent's office: They promptly let me out (and back in of course).
I had the same problem there. They didn't want to let me out after 2+ years on covid extensions (the whole covid extensions period, including the amnesty). Contacting the superintendent's office solved the issue: they promptly let me out (and back in of course).