What I see the main problem I believe, is your plant needs a bit of fertilizer. Without these chemicals no plant is able to make food for itself and thrive much less survive. Fertilizer does not nor should it come with soil. Just a tiny bit of balanced fertilizer, the one I always recommend even though I do not like the company, this is a great all purpose can't mess it up fertilizer. Extended release Osmocote 14-14-14. Use only half the prescribed application.
Plants have to have fertilizer added to their soil. Everything we humans do is inherently artificial. Crops, ornamentals, vegey gardens, indoor plants, terrariums are all artificial. The plants rely on us for their needs. Doesn't fall from the sky, compost is only for tilth in our of doors soil, adding banana peels, garlic or eggshells is nice but completely wrong.
Potted plants need drainage, water when the plant needs it not before, good soil medium that enhances drainage and air, great light because plants make their own food using the sun as energy and we have to make sure there is just enough, not too much of the chemicals; CO2, N, P, K, Molybdenum, Manganese, Ca, Silica, Fe, S, and at least another dozen chemicals. Without these chemicals plants will not be able to make their own food. They become susceptible to damaging insects and disease.
I hope THIS POT has drainage? No? Yes? I would buy a cheapo clay pot shorter than wide is best. Lift bottom of pot off saucer or surface using pieces of tile, flat rock. Water well and allow to completely dry out before watering again.
For your baby I would use a 6" diameter, 3" high clay pot. Just potting soil. Nothing else. The potting soil should not have fertilizer or water holding gimmicks, gels, sponges added. The cheapest is the best. No rock at the bottom below the soil for 'drainage'...ugh. Worse thing you could do.
Lift your pot and newly potted plant in potting soil after watering deeply. Remember that weight. When your plant needs water that pot and plant will feel very light. Time to water again.
As little water as this plant needs, I'd purchase distilled water to water....a gallon a month? Don't use tap water.
Edit: Checked out the potting soil and it should be fine to use. My only worry is that this is probably a huge percent of coco fiber and absorbs/holds water. Should be fine for your aloe. Your potting soil said it came with nutrients. That means chemicals, fertilizer. I tried to find the ingredients and haven't been able to pull up. Do not add any fertilizer until we can find what is already in that potting mix.
Your aloe looks anemic. Like it needs a bit of fertilizer. Otherwise your plant can not make its own food, do its own repairs, build roots to support itself during times of low light and there is no other way to 'feed' a plant. The plant has to be able to make its own food. Yet, your soil said they added 'nutrients'...chemicals/fertilizer. Which is not registering for me because you plant looks like it could use fertilizer.
Do not add anything, especially fertilizer until we can tell what is in your soil already.
The next issue would be light intensity. What window orientation does this plant have? Drafts? Does it get moved around a lot?