I cannot find with the new captions a way to fade them in instead of just appearing on the screen.
Which are you referring to ... burned-in captions, open captions, or text via the EGP for say lower-thirds?
So, you're working with Subtitles.
I'm one of those who avoided when at all possible doing captions in the 14.x & earlier versions as it was such a ... not intuitive nor easy process. Ahem.
So ... could you fade in subtitles before? We have subtitles turned on quite frequently at home, watching the 'telly', and truthfully I don't recall ever seeing subtitles/captions fading in/out.
Sorry. I don't believe there is an option. Can you make a request on User Voice?
There is currently no option for fade in.
In the prevous caption workflow, there was also no option for fade in. You could use a higher track and/or keyframing to create a similar effect. But in the new workflow, the caption tracks are locked above the regular video tracks. And they are no longer video tracks.
There are other threads already asking about the fade in etc. Some focus on the track option.