This I think perfectly sums up my experiences with TAP. I have flown them a few times on cheap J tickets and I find their in the air and ground service mostly fine especially for what I am paying but when something goes wrong they are mostly useless. I had some refundable tickets booked the summer of 2020 that I cancelled proactively when COVID hit. They were per the terms on the tickets refundable back to cash (I had screenshots), I even put in the request for a refund on the last day you could request cash refunds on the TAP website. I waited two weeks and then immediately filed a chargeback with my CC company. Thankfully TAPs incompetence worked in my favor here and they never responded to the chargeback so I got a full refund from my CC company.

To OPs point I had a very similar experience this year. I was flying from North America via LIS to another European city. I monitored my booking regularly, checked in online 24 hours before but when I got to the airport in the US the agent told me your connecting flight has been cancelled you will need to deal with it in Lisbon. TAP had done nothing proactive, not even notified me. I get to the lounge and call their number. Get a really nice lady who without asking booked me on another airline to get me to my destination. I was actually pleasantly surprised and thought maybe I had misjudged TAP. So I go about my business for a while and decided (not sure why) I better check that booking and it showed cancelled. So I call in again and get a different agent who said all I can do is book you on a later TAP flight (which was many hours later). She refused to even acknowledge I had been booked on another airline or explain why it had been cancelled. Again there was no notification on any of this. Still waiting on my EC261 claim (and I am not holding my breath).