How to copy the text displayed in an HTML dropdown list (<select>)?

I don't know about a script, and it may be a bit more work than you're interested in, but you can select the object and hit "Inspect Element" which will tell you where the dropdown is in the code. Then, right click on the "select" area that is the dropdown, and hit "copy as HTML". Then you can paste it to a text editor of your choice. It will require some manual cleanup.

This is by no means an optimal solution. But it is the best I have at hand.