First is nice when I get upgraded, but I'd rather take say Qatar Business than BA first.
That said, the headphones I has on a US Airways Business from Manchester to Philidelphia were amazing - far better than the BA ones, so much that I bought a pair (QC25s) while I was in the States.
What with 2020 I haven't been on a plane for over a year now, and I've been on 3 trips on a train, so I've basically forgotten what "out and about" headphones are like. I do wear one on my ear if I'm watching something in bed (hook over ear). Never seen any wireless ones, fortunately I haven't downgraded from my iphone SE so can still use them.
Yes: for some reason I missed "first".
The upgrade to at least business is probably worth it (budget permitting) for flights ≥8 hours, but going to first is probably diminishing returns.
You also get more legroom and a less cramped seat.
If you're flying "only" five hours this may not be a big deal. If you're flying >10 hours (e.g., across the Pacific), then it can make a huge difference to comfort.