no - it's a tiny fraction of the actual cost. so it's not "free" but it's massively subsidized to the point of being nearly free when it's a country paying for it
In a high-development high-capital low-marginal cost it's tricky to determine the "actual cost". The marginal cost is minimal. The opportunity cost is minimal too (not like the satellites over Ukraine could be providing connectivity for other congested areas).
You are going to have to do better than some tweet battle. AFAIU from Wikipedia with decent sources the service is free, but the terminal's not, and that is what Poland paid.
Also, it's not like Ukraine or even Poland has to pay, the can pay if they want, they can also not pay if they want. It's entirely elective. They can stop using any time they want. I heard that Google has a Starlink replacement in the works that is super awesome and I also heard that while Europe has completely killed itself with regulation they are entirely willing to buy things made by China which has absolutely no regulation.
