I have been trying to change the water every 3 days due to the aloe's potential to go bad.
I have been doing my best to keep her in the warmest part of the house each day which has managed to defluff her feathers when she is warm enough. She is still quite sleepy and depressed
I'm sorry to hear about Snowy. I do not really know anything about Budgies.I had walked past her cage about a week before she started getting sick and had noticed her seed badly needed changing. I tipped the whole lot out and gave her a fresh containerful. The poor thing was starving she was so keen to get to the seed.
You may also want to post your questions/concerns on the caged birds forums - people that keep this type of bird may have some suggestions as well. https://www.backyardchickens.com/forums/caged-birds-finches-canaries-cockatiels-parro.57/
I also do not know much about holistic care, so hopefully @Hen Pen Jem or @coach723 will chime in with their thoughts.
Keep in mind, my comments are my own thoughts, I am not a vet nor an expert and I also do not mean to sound harsh.
Birds that are sick need to be kept warm. I do see that you are trying to do that, but she may need more or continuous heat. If you have room in her housing, look into using a small heating pad that she can get onto/snuggle into. I'm not a fan of heat lamps, but a small reptile light may also be an option.
She needs to be hydrated well, then add food. Since she has not been eating well, a liquid bird formula like Kaytee Baby Bird would be good. While it sounds good to make a mix of your own, sometimes a specially prepared formula works best - they are nutritionally formulated to support bird health.
I would change the water every day, not every 3 days. As for adding ingredients to the water, that is up to you, but some birds will refuse to drink that. Provide 2 water cups, one with plain water and the other with the aloe. This way she has a choice.
I would also provide her with fresh feed daily. Put in a small amount, what you may think she will pick through or eat. This would be in addition to being tube fed.
It's very possible that she has liver disease, your suspicions may be correct. Yellow poop can be from a number of things from liver failure to infection. Antibiotics may help - you could try the Baytril as suggested, but that is not a holistic remedy as you requested several times. The vet offer antibiotics but it sounds like you did not want to go that route - if you have changed your mind you may want to give them a call and see if the offer still stands - they may be able to provide you with the correct medications that you need.
Lastly, I do understand that she is a pet and part of the family. After you correct the feeding/getting good nutrition into her and if you decide to give antibiotics - give yourself a timeline for improvement. If she does not rally, then it's time to let her go. Birds will hang on until they just can't (like anything). It's our responsibility as their keeper to make the decision about what is best for them, not what is best for our heart/emotions.
You probably have seen this, but it may help you determine the amount of fluids/feeding she needs per dayhttps://lafeber.com/vet/tube-feeding-birds/
I wish you well and hope the best for Snowy.
Just my 2¢