Adding soil to stems in solo cup? Or wait to transplant?

You don't need to do a thing. Why would you transplant it before it becomes root bound? Are you the kinda person that likes to live dangerously? Would you wash your car right after you washed it? No because there's no point. Same with your seedling. There's no point in transplanting it at it's current stage. Let it become a young plant in that container. Leave it where it is. After 30 days of it being out of the soil, then you can think about bumping up the container size. Seedlings aren't clones. They take way longer to grow up and develop root structure and leaf and node structure. Keep it watered with pH corrected water. After 2 weeks of above ground growth start lightly feeding with a dilute nutrient mix of about 250ppm. I wouldn't transpoant that seedling till it was around 5 to 6 inches tall.

If you don't need to do not. Really if it stretches and gets top heavy is when you may add some to support it. If it is supporting itself leave it be. The more you mess with it the better the chances of stressing it or stunning it.

I've never started in cups as the shock during transplant outweighed the benefits when compared to starting in finale containers.... I grow autos. I would say do what helps you. If the seedlings is stretching and if extra soil will help hold it up then sure add it. It's not stretching so it can fully support itself. I see no benefit in adding soil. The cup gives it enough of a rootball until your ready for transplant. I would say do what you want. No real benefit either way tbh. Goodluck on your grow! 🙏