Conditional alternate "Only show icon, no text"

[Doa]

Not sure if you ever got past this (or if you're still looking for a solution) but you can use a zero width space instead of an actual space.

Touchbar Widget disappears when Applescript JSON return value contains emptystring for text

This is a feature IMO. If you want to display nothing, you can return a zero-width space character: https://unicode-table.com/en/200B/