Just sharing my experience: some friends of mine of myself took the Buquebus boat service from Buenos Aires to Montevideo, then back from Montevideo to Buenos Aires on the same day in early January 2020.

1. None of us received an Uruguayan stamp on their passport upon passing the Uruguayan immigration (we went through 2 Uruguayan immigration officers) at the boarding port in Buenos Aires (RENAPER Buqutheebus), but we did receive an Uruguayan stamp on our Buquebus tickets.
2. On the way back to Buenos Aires, also using the Buquebus boat service, all of us received an Uruguayan stamp on their passport upon passing the Uruguayan immigration (we also went through 2 Uruguayan immigration officers) at the boarding port in Montevideo (Terminal de Buquebus Montevideo in Puerto de Montevideo), and the Uruguayan immigration officers did check whether we had received a entry stamp, which they found on our Buquebus boat tickets. For one of my friends, one of the two Uruguayan immigration officers became agitated when they you couldn't Uruguayan entry stamp (before realizing that the Uruguayan stamp was on the boat ticket).

This means that in my case when taking the boat from Buenos Aires to Montevideo, then back to Buenos Aires, the Uruguayan immigration stamp one's passport only once upon exit. The Uruguayan entry stamp is only on the boat ticket.

Just sharing my experience: some friends of mine of myself took the Buquebus boat service from Buenos Aires to Montevideo, then back from Montevideo to Buenos Aires on the same day in early January 2020.

1. None of us received an Uruguayan stamp on their passport upon passing the Uruguayan immigration (we went through 2 Uruguayan immigration officers) at the boarding port in Buenos Aires (RENAPER Buqutheebus), but we did receive an Uruguayan stamp on our Buquebus tickets.
2. On the way back to Buenos Aires, also using the Buquebus boat service, all of us received an Uruguayan stamp on their passport upon passing the Uruguayan immigration (we also went through 2 Uruguayan immigration officers) at the boarding port in Montevideo (Terminal de Buquebus Montevideo in Puerto de Montevideo), and the Uruguayan immigration officers did check whether we had received a entry stamp, which they found on our Buquebus boat tickets. For one of my friends, one of the two Uruguayan immigration officers became agitated when they you couldn't Uruguayan entry stamp (before realizing that the Uruguayan stamp was on the boat ticket).

This means that in my case when taking the boat from Buenos Aires to Montevideo, then back to Buenos Aires, the Uruguayan immigration stamped my passport only once upon exit. The Uruguayan entry stamp was only applied to the boat ticket.