As I have mentioned before, any change in diet will usually result in softer stools. It is not a concern unless it turns into watery diarrhea.
A transition to a new food takes a minimum of 1 month to see if it agrees with the dog. In example: energy level, stools, coat etc.
I switch foods cold turkey without any issues, depends on the dog I guess.
If the last food didn’t agree with the dog why do a slow transition?
Call your vet if you want, he will tell you the same thing (I predict).
PS: Maybe cut out the homemade stuff and keep it simple for now.
