I use headphones over my hearing aids every day. I like closed back phones with a large and softly padded seal. Currently using Beyerdynamic DT770 Pro, but also have several others including Sony wireless which I use over the aids.
I’ve worn various Resound aids from Costco for about 9 years and have always been able to wear headphones over them.
I currently wear Jabra Pro aids from Costco with M&RIE which can play back music from my Samsung Galaxy S21 Ultra Android phone, but the sound over headphones or through earbuds is vastly better than through the aids directly. The M&RIE in ear microphones are extremely prone to feedback at the slightest touch, but I don’t get any feedback from the headphones as long as they are properly placed over my ears.
For listening without my hearing aids (e.g., when mowing the lawn), I currently use a pair of Nuheara IQbuds 2 Max in-ear buds. These get programmed to your audio profile using an app that works much like a standard audiogram test. Nuheara claims they can improve hearing external sounds, which is definitely not true in my case, but they do a reasonably good job of equalizing media playback to adjust to your personal hearing profile.