Populating form field depending on button click

I'd like to have one form, containing a dropdown field, and select the dropdown value depending on the button that was used to open the form modal. I can provide different button texts in the shortcodes, but how would I provide data-value for example? In the form itself I can then use custom JS to distinguish the button that was clicked or - even better - make it somehow dynamic.

Who has done something similar before and is willing to give me some advise?

I have already asked support but we didn't come to a usable solution so far.