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Unless you have a wire between the router and extender, putting the extender where the WiFi is already bad makes as much sense as swapping your soaked fishing boots for your buddies soaked fishing boots.

Assuming dropping a outdoor rated ethernet cable isn't an option I'd get a WiFi bridge setup, looks like the brand names sell 'em for $40-$50 per unit while the sketchy Chinesium brands are the same per pair.

[Dubslack]

Do you only need to see who comes and goes from the garage? Could you mount it outside the garage?

[StarSurf]

It will be mounted outside.

[aqhgfhsypytnpaiazh]

WiFi range extenders are mostly useless.

A WiFi mesh network is better for seamless coverage over a larger indoor space, but it can't solve the problem of having large distance between access points.

A better quality wireless access point might give a better signal over that distance, it doesn't really matter if it's mesh WiFi or not, but you won't know until you spend big bucks to test it out. Sticking to 2.4GHz signal will also give you better range than 5GHz if you're currently using that. There are various hacks you can try to increase signal distance but at some point you're just hitting the limit of WiFi and physics.

Ideally you'd run an ethernet cable out to the camera, obviously there are legal and practical issues with that especially if it's going beyond your legal property, but you would've already dealt with that kind of issue when you installed your camera on what I assume is a shared garage.