How to check if a terminal can display undercurl from within a bash/zsh script?

How to check if a terminal can display undercurl from within a bash/zsh script? In a recent project I used undercurl escape sequence for output printed by a zsh script. It works well in modern terminals, but Apple's Terminal.app shows that as a reversed background-foreground. It would be nice to be able to detect if the terminal has the ability to display undercurl, and only then use undercurl or default to regular underline.