I’m also a FTM. As much as we hope for, it’s close to impossible to stay phone free these days. We managed to go zero tv time until our baby turned 3 months old. Then we started to play Ms Rachel for baby’s entertainment (she loves it!) and it serves as a background sound too (baby doesn’t really watch it when she’s playing).
At least your great grandma who is so so senior in the family hierarchy, is willing to watch the tv mute. For that, she has my respect.
Just bring the baby away to the room from time to time. Or get out of the house for a walk. That’s what we do.