In the bigger towns, with the chain supermarkets (Intermarché, Pingo Doce, Leclerc, Lidl, Aldi, Continente)--you'll find each of those chains has their own-brand foods with a lot of natural foods including vegan alternatives. I'd say Continente and Leclerc probably have the biggest ranges.
In the smaller towns with small supermarkets, your best bets are the canned or jarred (cheaper than cans) beans as noted above.
Restaurants/cafés are definitely a challenge. Even the soups mentioned above like caldo verde typically have a bit of chorizo added for flavouring, which is pork-based. And most of the vegetarian options they offer include either cheese or eggs or both.
But a fair number of younger Portuguese are vegans, and suitable products are becoming available.
There is a kind of sausage (I know; this sounds sketchy) called
alheira which avoids pork. Traditionally, it includes another meat-based source instead, but you can now get it in a vegan version. Also, another one, similar, called
farinheira.
The Prozis products are a recognized brand in the country; quite new, concentrating on plant-based food, I believe. You should check them out!
Here's the result of the Portuguese Prozis.pt website, searching for "vegan":
Bom caminho!