guess it depends on your budget but there are wired headphones that will last plenty long enough, just dont fall for "gamer" advertising or buy super cheaply made wired headphones where they are only wired to keep the price down.
aside from replacing ear cups every once in a while stuff like this will last forever from what I've seen while researching headphones, been thinking about getting these at some point:
https://www.amazon.com/dp/B088C19X96they're not cheap by any means, but compared to bluetooth headphones of similar quality its not that steep of a price either. there are obviously other cheaper options that will still last a while though, just do your research.
as for the whole audio delay thing, wired headphones are better for that, and though I dont know enough about bluetooth to say by how much, I think higher quality stuff does bring down the delay a bit. But when I would try to play mobile rhythm games with bluetooth earbuds, it'd be like 100+ms out of sync compared to my wired headphones, and the delay would change with how good the connection was.