Mine is 15 months, doesn’t walk at all but cruises and crawls at speed. He’s my second so I think less about what to do with him than his sister and they play together when she’s not in school but when it’s just us things he enjoys:
bath, he’ll do half an hour with an empty shampoo bottle filling and emptying it
sitting on a rug in the garden picking grass
he loves play dough, does it at the table while I’m pottering or working at the table
stacking shapes, magnet tiles, books, puzzles
I use a carrier a lot, a back one and a front one, I very rarely ever use the buggy. If he’s close to me he’ll do most things happily.
When I’m cooking I sit him on the floor with a wooden spoon and a plastic bowl and give him bits of veg to chew on or I bring his highchair in when I’m making bread and let him poke stuff.
I know what you mean about feeling the need to entertain but I find we’re both happier when I get on with stuff and just let him join in and then we have specific time reading, singing, having cuddles throughout the day.
He helps me fill and empty the washing machine, he helps me unstack the dishwasher by passing me things, he’ll sit by when I’m hanging laundry out, he plays with pillows when I’m changing the beds. I did the same with DD and she’s grown to help more and taken on things as her own jobs and it’s worked pretty organically.