D.B.
ETA: Just read your update that your husband is home but has stuff he needs to get done. Yet your son is texting you 10 times a day and wants you to come hang out with him. Don't you have stuff you need to get done? I'd nip that in the bud right now. He needs to grow out of the notion that child care (and child entertainment) are women's work, and that your paid job is somehow less important than what his father is doing. I know that's society's message, but it needs to stop. We need to raise more enlightened boys and men who see us as equals and not people whose work and value can be dismissed. A good 30% (maybe more) of our Mamapedia posts are about women feeling overwhelmed by the unequal division of roles at home.
Original: You've discovered the down side of all the planned "enrichment" activities that so many parents struggle to provide - kids don't know what to do when there isn't one. So they become sort of paralyzed with the idea that true enrichment comes not from someone else creating and supervising and directing the activity - but from being the one who does that.
I would go to the library and talk to the librarian (see if there is someone who specializes in the tween/teen years, but if not, go with the children's librarian). One of the best things we did for our son's birthday parties (which we limited to 6-8 kids tops) was providing much simpler entertainment that his friends' parents did. While they brought in petting zoos and bounce houses, or rented out gymnastics places - all of which cost a fortune - we got a book of party game from the 50s. The kids had a blast with potato races and other low-tech or no-tech options: 4 potatoes, 4 wooden spoons and a couple of broomsticks to mark the start and finish lines - well, that was a party. And we had other games just like it, plus scavenger hunts with silly clues. So I think, if you found a book of classic camp activities that use everyday household objects with maybe a few purchases, you'd have a hit on your hands.
You might also get a book on Rube Goldberg-type inventions - those elaborate set ups that use a mish-mash of simple objects to create something that does a simple task - like turn on a light or pour a glass of water. Let him have free rein to build something at home. You can find some amazing videos on these things as well, with university students creating incredible set-ups. It's not a kid thing at all.
I would say you may have to limit screen time more, frankly, because he's too locked into it and really feels the lack of it. I think you have to have a much firmer limit on text messages. Maybe 2 a day are okay, but otherwise nothing more unless someone is bleeding or something is on fire. That was our rule with our kid - even if I was on the phone (no interruptions except for blood and flames! With uninterrupted time, he built so many things by combining Legos and K'nex and other toys (half a day with a leftover helium balloon to try to get it to fly over the house with different weights suspended from it) that he became a civil engineer and went into project management at a construction company. I don't know what your living arrangements are, but we had a basement space he could take over, and some sections of the backyard he turned into his experimentation zone. He also had basic tools - hammers, screw driver, a bunch of nails and tacks, you name it. Your kid could start a garden (flowers or vegetables or both), make birdhouses or feeders to give to family or to a local nursing home that allows residents to have something outside their window. Our son took scrap lumber and some hex nuts and some nails and wood glue, and made us a Hanukkah menorah. Maybe yours could make Christmas ornaments for your family, his grandparents or the local homeless shelter. Maybe he could learn to cook and you could make a meal for a local shelter or take something yummy to the fire fighters or police officers, particularly the overnight shift. Maybe he could find out what the food pantry needs, and figure out a few healthy foods you could buy every week and put together a nice nutritious drop-off carton. Maybe he can enlist a few neighbors to help out too, or put together a list for your office or friends - "if everyone gave one thing, we could feed a family..." to encourage the small steps toward a larger goal...which is also what you are trying to teach him.
My kid is extremely social and has always has a great crowd of friends, but he's content with his own company. And that only happened because we informed him pretty early on that we were not his personal entertainment committee.
So, I'd give him a list of chores he can do if he's really hard up for fun, and tell him he can sit on his bed and ponder his terrible lot in life. You could also give him a library book or 3 of fun activities he has never tried, and help him understand that borrowing is fine - we don't always have to buy new. The library is the greatest underutilized resource in most communities. I'd cut him back to 2 texts per day. Extra texts? He loses screen time. But I'd put more emphasis on his ability to be up to the challenge, saying you have faith in his ingenuity if he just gives himself a chance. Creativity is hard at first, but his favorite baseball player or scientist didn't become an expert on the first day either. You could have a big goal he could work toward at the end of the summer, but make sure it's cumulative. He can't complain for half the summer, do a little work for a week, and wind up with a trip to the expensive amusement park, you know?