If you hold an Amateur Radio license it would be entirely legal for you to repurpose this hardware for transmitting in one of the many allocated amateur bands, as long as the standard rules were followed. (No encryption, always identify yourself with your callsign.)
There is a long tradition of radio amateurs re-purposing other radio hardware. CB radios can often be retuned into the 10 meter band, wifi transceivers can work inside the 13cm band, for example.
Once you get into this kind of special purpose microwave gear, it's all made to only operate at a very specific frequency. So in this particular instance, no the dish really isn't able to be used or repurposed for anything else. The only thing it is ever gonna be capable of doing is listening or talking to Starlink. There's no shifting it into a nearby amateur band as you can do with some wide bandwidth LNBs or old commercial radios.
And that is my entire point. The range that a starlink antenna can transmit or receive at is ~10.7GHz - 14.5 GHz. (possibly a bit wider than that, but not by much) All of which is licensed spectrum. And starlink only has a license for using that band if the beam is steered at least 25° above the horizon, and 25° away from the geostationary orbit band.
Good luck doing anything other than the intended use with that.
There is a long tradition of radio amateurs re-purposing other radio hardware. CB radios can often be retuned into the 10 meter band, wifi transceivers can work inside the 13cm band, for example.