I don't know very many games that go that overboard with background animations. It's more common to use individual sprites for the animated elements(like the twinkling stars). And I wouldn't fault the game engine on this one, as I don't know of any other engine that could handle this massive data with ease either.
If you really wanted to do it like video, there are extensions that can handle it, though I don't think any are free. GMS2 doesn't handle video natively. I'm thinking you are just going to have to rethink the way you this, either animating smaller pieces and overlaying them on a static background, or just doing many less frames.
Think about it like this. If I understand it correctly, GMS2 isnt' doing anything fancy as far as compressing image data for the GPU. So it is working with 32 bytes per pixel(RGBA 8 bytes each). That's almost 8MB per frame at 1920*1080. Which is over half a GB, just for that one background. I'm sure that's why GMS is lagging on you at that point. That 500 frame animation you were looking at is going to be just under 4GB. That's more RAM than a 32 bit PC can even use. Modern PCs have 8, 16, or more still, but see how much memory that is using compared to total memory? Then you also have the GPU's memory to be concerned with. If you aren't on a gaming GPU you aren't likely to have more than a few GB RAM on the GPU so even if you did get the game to compile you would be constantly swapping textures to the GPU. Your typical high-end 3d game doesn't try to do what you are trying to do on a 2d game basically.