Today the Thai-Myanmar border crossing of Mae Sai reopened. It appears to be the first "proper" land border reopening that should allow foreigners and Thais to pass, without being restricted to the border town or a border run (for certain foreign nationalities). However, it is noted that Covid restrictions apply on the Myanmar side and will apply for at least one month before they are re-evaluated. Everyone, Thais and foreigners will need either proof of vaccination or a Covid rapid antigen test done within 48 hours and this proof must be printed out. No electronic copies accepted. Another rapid antigen test will be performed on arrival in Tachilek at a cost of 15000 Myanmar Kyat. Only one day pass holders are exempted from the on arrival test. It is not known whether foreigners, who request a one day pass will be exempted or if this only applies to Thais holding border passes.
The link is only in Thai. I'm sure English language media will soon have their own versions, but they're usually delayed by a day or two.
TLDR : Answer Summary
The Mae Sai border crossing between Thailand and Myanmar has reopened, allowing both foreigners and Thais to cross without previous restrictions. However, travelers must present proof of vaccination or a negative Covid rapid antigen test conducted within 48 hours. On arrival in Tachilek, an additional test will be required, except for one-day pass holders, whose exemption status for foreigners is unclear. Current Covid protocols will be in place for at least a month. While some sources indicate a return to normal travel might be imminent, access is currently limited to Tachilek, with no travel to Kengtung allowed in the initial phase.