And since that property now belongs to the community, do the rental
fees they pay now belong to the community HOA? Where can I find info
about whether the carriers are paying rent (and how much) on that
There was one or more transfers of ownership from the non-profit until the ultimate owner the HOA. Those transfers of ownership should have been when the tower was addressed. But of course it might not have been included in the transfer of ownership.
In the late 1980's the company that was serving as the developer of a community that I moved into in the 1990s never got around to transferring ownership of the common ground to the HOA for $1. That land was used by HOA members, it was also the location of the sign at the entrance of the community. It was a buffer between a busy road and the first houses in the community. Then the savings and loan crisis hit. The ownership of the property ended up with the Resolution trust Corporation. It took years of lawyers, and thousands of dollars but we lost the property, and the new owner built a store on what was supposed to be common ground.
In another community I lived in the builder owned the "community" pool even after all the homes were built and moved into. They made a profit until the needed repairs couldn't be ignored and they then sold the pool to the membership for an extremely high price without making the repairs.
The HOA may need a lawyer to trace all the documents to see who has the rights to the rent.