I've recently bought a kitten. She is now 3 months old, and i've had her for 1 month. The first week i had brought her home, i was only feeding dry food (applaws kitten). I think she had mostly normal stool, but i didn't pay that much attention to it. It definitely was on the normal side tho, because i would have noticed otherwise.
Anyway, i soon started giving her wet food. I had nothing to use for transition, so i just started by giving little wet food, and gave a bit more every day. Since i started giving her wet food, her stool has become soft. It's not diarrhea, but it's soft enough (and a light brown), that a tiny bit always keeps sticking to her butthole. She has short hair, so it's not that poop sticks to her hair. The stool is just soft enough that her butthole remains dirty. I have found poop stains on many of my furniture already.

I thought that maybe it's the wet food itself that causes this, so i eliminated it, feeding only dry food. After a week of feeding dry food only, it didn't get better, so i thought maybe it's the protein (chicken). I gave her other dry food for 3 days (rabbit and salmon). Earlier she used the litterbox, and when she walked past me, i instantly smelt that her bottom was dirty.

Earlier it occurred to me that maybe i'm just switching foods too fast?
Is it necessary to have a transition period when switching dry foods as well? Should i even do that, considering she already has soft stool anyway? For how long should i feed the same specific food, before it would affect her (and change her stool)? Is there a protein that many cats are allergic to? Or in other words, is there a protein that is especially recommended for cats with allergies?

Long story short, i can't seem to find the reason for her soft stool. What is the best way to find the source?

Thanks