I haven't used ChatGPT in a long while, but when I did, you could include something like "In the style of William Shatner as James T Kirk" or "In a very fun, casual tone" or etc to any prompt and get that in your reply.
I realize it is not exactly the same, nor does it solve your tech issue if it's not even offering you the dropdown choice from the other screenshot, but I never tried anything like that via prompt which didn't seem to work.