correct. I am from Netherlands -same. When you get into the COE form you can choose which visa category applies to you - choose “visa exemption” , i think it is category 11 or 12. When on COE site, fill out personal details, upload passport, picture and bank statement. Then submit for phase 1 confirmation. After that, arrange asq hotel, flight and insurance, and upload that. Easy. Also get RT-PCR test and fit to fly certificate before you fly, fill out T8 form and also download the Thai corona app. It all sounds a bit difficult but if you study the official sites it is actually quite easy
Yes you can apply based on visa-exempt. But you still need to go in quarantine upon arrival in Thailand. Including quarantine period you can stay 45 days but when in Thailand you can apply for a 30 day extension. Check out the official websites of the Thai Embassy in Roma for details.