You would think it be easy or an obvious option. Perhaps they will add it in at some point. For now, I found this article that might help.
https://indesignsecrets.com/live-captions-with-autofit-transparency-effects.php
Another option:
The only other way that I know how to accomplish this is by creating duplicate paragraph styles. The first paragraph style will have the shading turned on and both the color of the text and shading should be the same. Result is a solid block of color. At the point, select that text box and copy. Then under FX panel lower opacity to desired percentage. Now “Paste In Place” and this will put a copy of the text box on top. You will now create a copy of that first paragraph style and apply it to that text box you just pasted. In the settings of the second paragraph style just turn off the “shading” and change the color of the text to whatever color. Sucky work around but it works.