I have done both.
I do not do any work in the garage connected to the house. I have a ton of workshop space I use in separate buildings.
James is the expert but after the mini-split stopped working in the shop, I replaced it with a window unit to cool and heat two bays very cheaply compared to replacing the older unit.
I do augment everything with fans, btw. It works. Maryland get hot and humid so I know the drill.
I also have a smaller shop that is directly attached to the barn shop that I have cooled with a small window unit for over 20 years - same unit. I was up there for hours today getting organized and fingers crossed I get to 21
Do you still live in the house in the photo? Nice.