As far as I'm aware, Pousadas in Portugal are no longer a state-owned affair. I think they were sold off to a private hotel chain - Pestana, perhaps? - a few years ago.
yes, Pestana. They still email me. The one north of Porto in Viana de Castelo, on top of the hill overlooking the port is very nice. Well it was in 2018 and the half board rate was similar to Paradors at the time. Not looked at them since as too busy exploring Spain.