I finally found the hint I was looking for.
This video provided some syntax on how to work with component values: https://www.youtube.com/watch?v=TbAZHvB5NEk&ab_channel=Microsoft365PnPCommunity. Most importantly, I learned that I needed to wrap my output in a template tag.
Adding template to my search led me to this page: https://quares.ru/?id=256232. If you're like me and can't read Cyrillic, this link should help: https://translate.google.com/translate?hl=en&sl=ru&u=https://quares.ru/%3Fid%3D256232&prev=search&pto=aue.
Hopefully this will help anyone else who's struggling to read the values from the People Picker selected person.