Well TBH, I have been exclusively using Bluetooth headsets for like 7 years now and I’ve had a good experience with that.
I would recommend either big clamshells (I use a rather expensive but awesome Bose 700) or necklace designs like my LG tone 800 hbs headsets (I got like 4 of those over the years). I bought a pair of extremely expensive Sony WM-1000XM 4 that suck donkey balls for a long list of reasons, but not Bluetooth.
Barring some connection issues sometimee, Bluetooth is really quite nice and allows me to walk around freely. I haven’t missed the jack plugs ever, really.