Portugal for a month in Feb or March

I would aim for March over February; the days will be longer and you will have a higher change of fair weather.
I would also skip the Algarve, especially if your trip is closer to 10 days than to 14 days. 10 days is just enough time to cover Lisbon + 1 day trip, Porto, and a stop in between (e.g. Coimbra).

In 2023 we wintered in Portugal for 3 months ( 2 in the Algarve and 1 travelling).
Wrote a trip report that might be helpful to you if you want to check it out.
https://www.fodors.com/community/europe/extended-trip-to-portugal-1711933/

You could take a look at Madeira which is an easy flight from Lisbon (under 2 hrs).

I spent the second half of February last year in Carvoeiro on the Algarve coast. We did lots of walks along the coast, and car trips to other small towns on the coast and inland. We also spent time on the beach, including in the water. For this Canadian, 20 degrees and lots of sun was plenty of escape from winter back home. We also spent a couple of weeks around New Year’s in Lagos prior to Covid, and enjoyed similar weather.

March is usually better weather but anything will be better than Canada. If you want to do the Algarve, stay in a bigger town and you should be ok. I stayed in Lagos a few years ago in March and found plenty to do. You will need a car in the Algarve, though.

Every part of the country will have more rain - hopefully. But, you should still have sunny days. Évora plus towns in the Silver Coast area might appeal to you. I prefer this area to the Algarve, personally. You might want to do a bit of research on this area before making your decision.