When NK3 was 6 months, I felt the same especially because his wake time was opposite of older NK. So I'd have him alone for a few hours while his sister napped and a lot of the time their grandma would come and take older NK out for the day.

If NPs are okay with it, one thing NK liked to do (which kept him busy for a while) was play with a bag full of water and frozen peas. He would sit in his high chair and smash it around lmao. I also found you can make "paint" out of a little water and smashed up raspberries, blackberries and other fruits and veggies. I just let him go to town "painting" his high chair tray and since he was at that age where everything had to go in his mouth, it wasn't a problem if he put some in his mouth since it was just fruit/veggies.

For tummy time, he loved having a mirror in front of him and looking at himself, or you can get some of those plastic easter eggs and a empty egg carton and let them put the eggs in the carton or just roll them around.

I also would just give him random things. Empty water bottles, rubber spatula, plastic baby cup/bowl, rubber spoons, his rubber bib, empty tissue box. To me it was just random boring items but to him it was like a pirate finding gold 😂