A.M.
I have had to go right back to work, so I do not speak well to the staying at home part. ( although I got to with the oldest) I would say do what you are doing, but have baby in the sling. They L. to be held and touched and they can hear your heart. When I do this no matter what I am doing he is included. I wear him all day long pretty much.
I also make diaper changes a play time. We do "run run run these little legs" ( doing the running motion with his feet and legs) then "dimples on the knees" (touch his knees) " and Jump as high as trees" ( lift him up out of his diaper to change it) I do this before I change him, while I change him and after. He looks forward to being changed instead of fussing.
I also other times talk to him while changing him and just tell him how wonderful he is and how much I L. him. I also say in a funny voice he loves " time to change the baby, what are we going to change him into? A baby with a clean diaper" He laughs and so do I
He also likes a game where you set him on your lap facing you and you say " a smooth road a smooth road" ( while moving your legs back and forth under him with out going up and down) then "a bumpy road and bumpy road" ( up and down just a little) " a rough road a rough road" (up and down a little wilder, still with care) Then " a hole in the road", (and you move your knees apart and let him drop just a little while holding him) Babies L. to have you do this over and over they think it is funny.
Show him things, talk to him about things. Engage him in conversation. At first it may feel funny, but he will L. it and it will lift your spirits too.
Also if you are at home do not become isolated. Go to LeLeche League meetings, join a MOPS group. Volunteer and bring him along, consider working part time doing something where you can bring him along ( part time nanny or something like that)
Do treasure the time, you will never have another like it with him and you are blessed to be able to just be home with him, I wish I had had this option with my last 3, even though I L. my work and even though I get to take them with me, I would L. to also have the option of "just being a mom"
You are smart to be reaching out. I would also recommend that you wear him out on a walk when ever you can.