Yes, Chiang Rai I meant 😂 . Oh well, you have your ticket straight to Mae Sai now for Saturday. But in future, if the tickets to Mae Sai are sold out, you can get the greenbus to Chiang Rai then get the local bus feom there (I usually do this anyway, give my legs a stretch and have a beer)
That's to Mae Sai bus terminal for Saturday yes, but you could gwt the greenbus to Chiang Mai bus terminal tomorrow, then get thw hour long ba to Mae Sai bus terminal
Why not get the greenbus to Chiang Rai, then get the local bus to Mae sai,mit cost's about 30 baht and takes and our. It's comfortable enough, and cool with all the windows and doors open.
If your visa expires out on a weekend and you go on the Monday, they extend it from the day it expired, and no overstay charge, I've done I many times.
If it runs out in the week and you overstay, they extend it from the expiry date, and you pay however many days you have overstayed, I've donw this many times.