Total mental presence with children all day is unsustainable. Brief mental absences during the day — phone, book, quiet thinking time while children play near you — maintain capacity for engaged presence the rest of the time.
Why this isn't bad parenting
Children benefit from independent play (developmentally important). Parents who never disengage burn out and become less present overall. The pattern of total engagement is unrealistic and damaging.
Aim for 30-60 min of 'parallel time' daily where you're present but mentally elsewhere (and children are safely playing or doing their own thing). Sustainable parenting requires it.