Pre-covid the airport authority had a free half day tour into Taipei (morning) or some traditional village near the airport (afternoon) for people with long layovers. Although there is also a pretty easy direct train into the city, if you wanted to do your own thing.

Also there are some secret free showers, even for economy passengers, hidden along the hallway that connects terminal 1 and 2 on the airside. Also also there are free massage chairs at some gates. TPE isn't as new or fancy as some other airports in Asia, but they do a really good job making things nice for passengers. I would absolutely be happy with a long layover (assuming covid rules allow for casual entry).