Caveat: I've flown TAP several times, always short- and medium-length flights (not trans-Atlantic) but have followed them for a while.
TAP is a slightly unusual airline, although maybe less unusual than you might think. Not well known by Americans. They are a legacy, old-school, national carrier – Portugal's own flag carrier. So in some ways, they're like any legacy old-school carrier. Big network of flights, you can fly TAP all over the world (South America, North America, Africa, short-haul all over Europe). They have modern, new planes (not all of them are though), even a nice business class with lay-flat beds on efficient, brand-new jets. But they also offer rock-bottom prices and sometime behave like "low-cost carriers"; sometimes their service can be minimal or spotty -- they have "unbundled" some things as cheap-o airlines do.
In truth, TAP follows a kind of hybrid model, between big old legacy airline and small cheap cut-rate airline. This model exists more in Europe than it does in North America. Aer Lingus (Ireland's national airline) follows a similar hybrid model.
I like TAP. I've never had any issues with them. You can often catch surprisingly low fares on them, but you do need to be aware that the low fares may come with "unbundling issues" (eg you pay extra for anything other than minimal baggage, maybe you pay to pick a seat, etc). It depends on the ticket you choose. Just don't expect more than is specified for your ticket -- pay attention to what is and is not included, what might be extra. The details should be easy to understand, it's all on their website, just don't assume you'll get things that are not specified.
I had to cancel some flights on TAP during the pandemic, they answered the phone quickly, were easy to deal with, and refunded my money as promised. I've received what I considered good service, but of course I've seen others complain.
I would fly TAP again without any hesitation, but anyone contemplating flying with them needs to read the ticket details and limitations carefully (this is increasingly the case with any airline).
Hope that helps. Portugal is lovely, you will enjoy your time there.