I was recently in Portugal on hols. It’s a lovely country and I’ve been a couple of times. The area of Algarve near Tavira toward the Spanish boarder is super but most roads quite narrow and cars do drive fast so unless you veer outside the bigger roads to farmed areas it’ll fee quite busy. Do have a look at past tour of Algarve routes and you might find that most of the 2023 or 2022 editions have ridden on decent quality roads although some would be really busy since they aren’t closed off outside of racing.
This time round we were near Lisbon but I felt the same about traffic, not too safe, so I rented a MTB and had fun riding through farmland and forest areas with no traffic and some awesome sights. I mostly ride gravel so this complemented gravel in a nice way whilst feeling really safe and is what I’d recommend. There are some bike paths by the coastline near Lisbon such as heading north from cascais.