We are allowed to put a satellite dish on condo roof.
Contractor requires customer to sign an indemnification for damage to tile roof.
Therefore, the tenants got cable instead.
Just because law requires them to allow, doesn't mean it will be feasible.
(One of our tenants was the exterminator. He said cable company was a good source of business for him, because they always drilled a hole in the wall and didn't seal it, providing access for rodents.)
In this case, although there is an HOA, it is OP's own house and roof so not such an issue.
Do HOA rules dictate color of shingles/tiles? (probably)
If solar shingles/tiles were installed where facing street (and sun), that might be allowed (but not necessarily cost competitive.)
I've seen some in my area which blend in well.
Likely, HOA will allow panels in some location when presented with the law. But it will be the surface of the roof facing North, which will only produce power in the summer. If you could mount panels as an awning off the eaves in back then they could have a better tilt.