Hello and welcome to the forum. I am sorry that your dog is so very poorly. For anyone who is not familiar with Malassezia, here
is a description. I have a very good idea of what you are going through because I have dogs in the past with colitis and skin problems but not together in one dog. The most recent one was a rescue who had extensive ear surgery as a result of neglect (before I had her). Much of the time she was in baby socks using a home made sock harness as described here
I got that information from Dermapaw
and used their product. I used to wash and dry her feet every time she came in from a walk then apply the ointment and put the socks on. In time I got her feet in good condition. Sometimes I had to use one of those inflatable collars to stop her chewing.
It seems that you are looking for supplements for the colitis. I understand that Pro and Prebiotics need to be canine specific. David has written about Priobiotics here. Bionic Biotic
seems to get good reviews. The My Itchy Dog website has useful information but as you say, it is easy to get overwhelmed. Yesterday our member Seaweed posted this thread
about a new company to the UK called AniForte.
I haven't studied it all properly yet but they seem to have a wide range of supplements so you might want to have a look at that. It is important to just try one thing at a time for proper evaluation.
I can see why the vet suggested bran for the anal gland problem as normally fibre is recommended. I do not know whether it will exacerbate your dog's skin condition. Most of the things that add fibre to the diet are carbohydrates e.g. brown rice, oatmeal, sweet potato so maybe bran would be the better choice. You can but try it.
One of my current dogs has had long standing skin problems but not as bad as yours. She is currently OK but in the past I have found that medicated baths (sometimes weekly) have been most helpful. The two shampoos that I use are Sebocalm because it is soapless and when she has had flare ups I use Seleen. I used the latter many years ago on a Westie that I had and it was always useful. However, as you probably know there are other shampoos specifically for yeast problems. From what I read, dogs excrete toxins via the skin so regular bathing is useful, and indeed necessary for getting rid of them. Bedding too needs to be washed regularly. This particular dog was also treated with Yumega Plus (now Yumega Itchy Dog) and I found it helpful. The reviews are usually very positive. Luckily, she doesn't need it now.
Food wise, I cannot suggest anything because it would appear that you are already using food that is appropriate for the problem. However, if you feel that it is not helping and you would like to try something different, please let me know and I will ask David, the site owner if he can think of anything else. The only other thing to mention is that I wonder if it is time to consult a veterinary surgeon who specializes in dermatology.