When I first learned to play and sing at the same time I started with simply talking while playing. I had a tough go of it at first; I’ve played for years, I’ve “sung” for years but never both at the same time. I would be playing and I would start to sing and then my hands would forget what they were doing.
Start your strumming, get into a good groove with it and just try to have a simple conversation. With singing you have to remember specific words and hit specific pitches/notes while trying to play a specific pattern. I really feel that small intermediate step helped.
Drummers talk of “Limb Independence” and I think it is similar where your hands almost have to be on automatic pilot to free your head to sing. It takes a bit of effort but start simple and work your way up.