Dartin for Divorce

Oh there was no way to get a Jack to lift the old beams, at least no Jack I could have gotten would have been tall enough. From my basement floor to that joint it’s like 12-13ft.

The floor feels pretty solid now. I probably should have checked the rest of the house. We luckily have a drop ceiling in the basement

Floor jack and a 6x6 post works wonders. I usually block up the the jack so it can't roll away or get bumpd out. A few 2x4's crossing under the jack usually does it.

That looks like bug damage, scary. Any wood dust on top of the drop ceiling tiles? If so, I'd be hunting for an exterminator.
If the damage is spread along the whole length of the joist, I'd be working toward adding new joists between the existing rather than sistering rotten wood. Sistering can work, but all the load goes through the fasteners so you need an absolute crap ton of nails/fasteners. Even then, nails have little to no axial strength and screws have little shear strength. You can through-bolt with 3/8 or 1/2" fasteners to get some clamp, but then you're only bearing on the hole the fastener goes through and wood has a horrible way of tearing out. Flitch plates (steel plates) can be added to help add strength but that's not cheap..
Rather than try to engineer a way to fix failed wood boards/beams, replacement is more reliable. Since you have access, I'd definitely go that route.
A couple floor jacks, or go buy a couple lally columns to build a temp beam support to act as a temp wall across the middle of the joist spans. Rip some ply to act as a spacer under the joists to the beam to leave you some working room to place the new joists or order up some engineered i-beams that aren't as tall and then pad them on the bearing ends to get them tight to the floor. Glue them up to the underside of the floor sheathing rather than trying to shoot screws or nails and leave the old joists in-place unless they're harboring pests.

I'm no pro, but I've been down that road a couple times.