Over ear bluetooth headphones advices

Hello everybody, I am looking for a pair of headphones with bluetooth and that can be used wired as well.

The bluetooth would be useful while traveling and while outside, but I would like to used them for work, at the office, as well as in my spare time at the computer at home for some gaming and watching films.
I was into the Sony WH-1000XM4, but I read I have to keep them turned on while wired to have the possibility to use the microphone (I know a solution to this is to buy a cable with built-in microphone) and if not turned on the audio quality drops significantly.

Would you guys have a good solution? Is there a pair of headphones that can fit my situation of not keeping them turned on while wired?