I'm in the U.S. and have tried to make flight reservations (for October 2021) using flyTAP.com. After finding an available flight, their booking engine presents a glitch when you try to enter your DOB and other information, so that you are unable to complete your booking. The same glitch also prevents you from signing up for an online account.
When you try to call their customer service number, either direct dial to Portugal or the U.S. 1-800 number, no one ever picks up. Entering your number for an agent to call you back also yields no results.
They do list their Facebook page, Twitter, and Skype account as online contact options, which seems rather unconventional.
In sum, this certainly doesn't seem up to par with modern customer service standards. I realize that they are a nationalized airline. What's up with TAP Air Portugal?