Assign Photos.
I have iOS 15.5 on my iPad. I was having the same trouble as many of you. I figured out how a different way than I have ever used before.
1. Create the new Album first. 2. Open the album you just created. You will see a medium large + sign inside the album. 3. Click on the + sign. That will take you to your photos. 4. Click on the photo or photos you want in that Album. A small check mark in a blue circle will appear in the lower righthand corner of each picture you choose. Click "Done" in the upper righthand corner of that window. Voila!
I hope this works for at least some of you. When I included the word click, of course I meant "touch with your finger."
iPad Pro, iPadOS 15