We have the original TT battery it is going on five years old. When traveling we have discovered that our battery lasts about two or three days. Since we rarely camp off grid this is usually sufficient.
The very few time we have intentionally been off grid for three to five days, I bring my trolling motor battery or if it is an unexpected stay, I simply gained another night by hooking up the jumper cables to the truck and TT battery and ran the TV for 15 or 20 minutes. The 7 pin connection does not charge as fast.
In answer to your question, what ever deep discharge battery your TT manual recommend is one that will do the job.
As mentioned if you plan any extended off grid, that is a whole difference story and battery power becomes a serious concern.
RVers do get caught off guard once in while, so you have too improvise like the rest of us.