Using the Figma desktop app for Mac, I added a new team member to a Figma Team. They accepted the invite and they showed up in the list of team members. (Side note, the number listed in the Members button stayed at 8.) I clicked on their existing role (Admin) but there was no option to make them the Owner. I checked all the other team members and the Owner option was available for everyone else.
I closed and restarted Figma and the number in the Members button went up from 8 to 9 and the new member could now be made an owner. That resolved my issue for now, but this seems like a bug that might be worth fixing.