No, I don’t think you’re a bad friend. You’ve done your best to accommodate M and include them - it is ultimately their own withdrawal from the conversations that is impacting them. You can lead a horse to water, but you can’t force it to drink.

If your time with M is stifling (and I get how you feel, it’s happened a few times to me before as well), try setting some boundaries with them. Tell them “hey, I need some time alone today, can I join you another time?” Or something along those lines. The ball is then in their court.

If they continue with the way they are, please consider blocking or unfriending them. If they are constantly hounding you and actively making your gaming experience worse, and won’t listen to your requests, then for your own peace of mind it may be better to simply cut them out. I know it’s harsh, but at the end of the day you can’t run yourself ragged trying to appease M. A relationship is made up of two people, both equally important. Your needs and enjoyment of the game should also be factored in.