Ok the keyboard and text Input Field disappearing doesn’t seem to be an Messages only issue.
Try swiping instead of tapping the „back“ button in the top left corner to go out of a conversation and back to the contact list. Next you go back in any conversation and the keyboard and text Input Field will be gone. Happens on WhatsApp for me too!
View attachment 936616
Tried it and not replicating on my iPhone 11 Pro