I've flown back to Thailand twice in the past month: from Vietnam to Don Muang, and from Malaysia to Suvarnabhumi.
On both occasions, airline check-in staff asked passengers to present their vaccination certificates (either in paper or on the phone). It was just a glance, not an in-depth examination.
On arrival at Don Muang, the corridor from the gate area heading to immigration was blocked by Ministry of Public Health personnel who checked everyone's vax proof as they passed (again, just a quick glance). At Suvarnabhumi, on the other hand, there was no check of health information at all on arrival.
The government had said they would only be doing random spot checks, and that was indeed my experience. I have no idea how either check-in staff or arrival staff handled unvaccinated pax, because everyone I saw (only a small percentage, of course) had a vaccine certificate.