You can get a Ricoh G900 II, which was released earlier this year, for sub-$800.

It's also fully automatic and doesn't require you to do much with knobs and dials. And it's waterproof!

I suspect you'll complain about it though.

No changeable lenses and not a full-frame sensor, does not support RAW.

I'm seriously interested in buying a reasonably-priced modern mirrorless camera with GPS. I'm not joking, I've been looking for a while to replace my old Sony Alpha.

I recommend Olympus for that. They're reasonably priced, generally more technologically progressive than bigger brands like Nikon, Canon, or Sony, have a small form factor owing to their Micro Four Thirds sensor, have GPS, and still have a decent set of modern and legacy lenses (which are also commensurately lighter and smaller than similar lenses on APS-C or full-frame systems).

I tried to check and it looks like the only model that fits is Olympus E-M1X ($2k on clearance sales). And it's 6 years old by now :(

Anything newer is $5k+. Or does not have replaceable lenses.

Is the 6 years old point relevant to you?

Kinda? I want to replace my 7-year old Sony Alpha with something out of this decade.