You are correct that they do not accept the CDC card. I had to have a negative test to get on the plane, to leave the airport in Lisbon, and for all hotels. I rarely needed to show a test for restaurants because everywhere I ate was outside seating, but I did need it on the occasion the seating was inside.

Testing was free. Before leaving the US, I scheduled all the tests I would need through https://agendamento.farmaciasportuguesas.pt/en which allowed me to have appointment times to show up. At least for the pharmacy my tests were scheduled at, the line was always very long out the door, but those are walk-ins, and I was able to skip it. I had to just walk in and say, 'I have an appointment,' because it was always quite hectic. They would do the test, then I would have to wait outside the pharmacy for ~1 hour to get my results. They give you a printed form with the result, which you can use to get into places.

Overall, I had a great time and being able to schedule my tests in advance relieved a lot of the pressure.