Here Is my 0.02.
Go ahead and store it in the garage. Would it be better in an air-conditioned house? Definitely. Is that always an option. Not at all. I live in the Florida panhandle less than 10 miles off the coast. The humidity is bad but as long as you take precautions you’re good. First off, follow the instructions of g.willikers with the oiling and storage. I do something very similar and have not had a bit of rust show up on any blued guns. That includes the one with less than perfect finish.
Theft is the real issue you have to be aware of. Make sure you take advantage of ALL available bolting options. I have mine secured to the concrete slab and the studs in the wall. It is also a good idea to integrate the safe into the fixtures in your garage. I made a slot in my shelving units where the safe fits snugly with very little clearance around the edges. I also took the opportunity to make a faux cabinet door to disguise it so someone would have to be actively searching to see it.
I also changed my behavior. I used to keep the garage door open to the street all the time just because I could. That changed. I now only have it open when I am in there or actively working out of the garage. I also make the effort to only open the safe when the garage is closed.
So by all means, leave it in the garage but be aware that you will need to work around it and change some behaviors to make it more secure. If you have the viable option to bring it into the house proper, then please do. That will save a ton of work, worry, and change.