The House and the senate can set their own rules. There is nothing in the Constitution about non-voting representatives in the House or the Senate.
The Puerto Rican delegates are there at the invite of the House. The House is intended to represent the people/citizens of states of the USA. It is a small step to also wanting to represent citizens of the USA that are not citizens of any state. It is, therefore, perhaps, unsurprising that the House would invite observers from major territories like Puerto Rico. The people in Puerto Rico are citizens, but have no vote in the House as only citizens of the states are democratically represented.
Moreover, there is a tradition of the territories sending delegates to Congress, going right back to 1787. But the delegates, representing the people of the territory, (not the territory) are delegates to the elected chamber: The House of Representatives.
The Senate, which was set up to represent the states sees no need to to have invited observers. Puerto Rico isn't a state so it doesn't have representation in the Senate.