This link provides instructions for getting in ROC passport if you are currently in the U.S. https://www.roc-taiwan.org/ussea/post/1410.html
You can use Google translate to read it in English
Note instructions may differ by TECO office.
A passport enables you to enter Taiwan during covid.
To work you will need a work permit or household registration.
To get health insurance, you will need household registration.
@tando, thank you very much. That page is very useful. I found links to instructions for applying for a Taiwan passport if you are living in Taiwan, which I have not seen before. It also has information helpful for people not living in Taiwan.