If they’re not part of the US, who are they part of? Because they’re not considered a sovereign nation on their own, and they’re not part of any other sovereign nation.

The US president is their head of state, they have a resident commissioner who is a member of the US house of representatives and although they can’t vote on legislation they can introduce it.

And as far as incorporation goes, although officially PR is considered to be unincorporated, there’s an argument to be made that various acts of congress over the years have effectively incorporated Puerto Rico, for example, Gustavo Gelpí argued just that in his opinion in CONSEJO DE SALUD PLAYA DE PONCE, et.al. Plaintiffs v. JOHNNY RULLAN, SECRETARY OF HEALTH OF THE COMMONWEALTH OF PUERTO RICO