The soil looks too peaty. Mix equal amounts of perlite and that soil for a quick fix. Also, how are you watering? That first pic shows what appears to be wet and dry soil. For my aloes potted with a very fast draining mix I set them in a bucket of water for about 15 minutes and then don't need to water for another 3-4 weeks when they are indoors. YMMV.

tj

That brown-red tinge is how they respond to too much direct sun too quickly. Generally, the best plan is to move them slowly, where they're in their new sunny spot for only one hour on the first day, then two hours on the next two days, then three hours on the fourth and fifth day, and then full-time by the end of the week.

The presence of pups is a good sign! It means the roots are nice and healthy. Some aloe vera plants can't manage heavy peaty soil very well, while others tolerate it reasonably well. I think it has to do with other cultural conditions like room temperature, water frequency, type of light, and so forth. A 1:1 perlite to potting soil mix would make it happier, I agree. But the color of the leaves is a sun response.

My own aloe went from indoor SE window, which was a lot of shade, to a SW window with fierce afternoon sun, to a place outside in all day dappled sun. Even with acclimation, the leaves went that weird color each time but became nice and green again once it adapted to the new situation.

Do pay close attention to its new water needs. It'll want more in the warmer brighter window.

I'll chime in with Sage. It's definitely too much sun, too soon.

Aloes need time to adjust/transition to more sun exposure. I personally keep mine further away from my windows because I've never successfully moved them to brighter light without burning them!

Amy B that cactus mix should be perfect for Aloe!

Crenda good to know about the soil.