I won't debate more on the finances because, like you said, they're a private company and we can't know for sure. However, reliable public estimates show starlink is profitable already or will be very soon.

Falcon Heavy is supposed to be cheaper per ton, yet somehow is almost never used for Starlink or anything else

Starlink already about maxes out the fairing capacity of the Falcon Rockets, so allowing more weight doesn't do much besides increase cost. Same with other companies buying launch services from SpaceX. Usually they don't need the extra capacity or margins heavy offers, although I wish me got more launches, they are always a treat to watch.

Starship isn't even projected to be cheaper than Falcon 9

Maybe not, but that wasn't my main point. They are already spending money on Starship and that isn't going to change. It's just soon they will actually be able to use that money they're spending to make more money by launching more starlinks. With the significantly larger payload capacity, they will also be able to launch way sats per launch and also more capable sats with higher bandwidth or more onboard propellants for a longer operational life

I expect Starship will be used to launch many batches of Starlink while the vehicle is still in testing and expected to fail on occasion, If you think about it in that capacity, the launches are free since they are already going to be doing test launches.