I wouldn't say I am burnt out personally, I would just say I've lost interest in the game. Sounds like it's similar to you? And sadly I don't think there's any cure for that, beyond well... Them not treating the game like an algorithm.

I login a couple hours to say hi to friends, do a few things like roulettes, and just generally have a bit of banter. Outside of that there's no real reason to login.

My suggestion is just play other games. I've been enjoying other titles... Some older games, and some newer ones on my backlog of games. Most of them aren't fantastic by any measure, but when you're diversifying, it hardly matters as much (and IMO FFXIV has been overhyped for well over 6-7 years).