Sion's HP stack have a cap still?

I never ran into a cap on the old Sion, or any of the champs that can increase a status effect. They essentially have unlimited power in them.

Yeah, there never has been a cap to Sion's bonus HP. Just like there's no cap on Veigar's bonus AP or Nasus' bonus Siphon Strike damage.

There is likely a mechanical limit to how high any stacking ability can go, but is there a realistic one?

Depends on if playing one game for a full 20 hours is realistic to you or not.

It's capped at a very large amout like 99999(I forgot the exact number, but i'm sure it's not a cap that u can reach)

The only limit to his max health is how big of a number the programming can address.