Thai embassies around the world have started posting an update to the information needed for foreigners if they wish to enter Thailand between 1st April and 30th September 2021.
If everything goes well, we can presume that they plan to fully re-open the country on 1st October.
The Special Tourist Visa (STV) will cease to exist from 1st October. If things go to plan, people can enter without doing a quarantine.
But they will need a vaccine certificate much like some people still need a yellow fever-free certificate if they come from certain countries.
Source: Richard Barrow in Thailand