I can’t answer 100% for integration with KyivStar, my colleagues will help here, but most likely yes, you will need a separate server.
In general, OneBox is far from the system that should be put on shared hosting.
This is not some simple engine a la wordpress (yes, wordpress is also not a simple system, but OneBox is heavier by a couple of orders of magnitude).
For example, for the same hetzner, virtual machines start from $3/month -
https://www.hetzner.com/cloudThe norm of a virtual machine is $10/month.
Also, I do not rule out that the next versions of OneBox will not work at all on shared hosting.