I dont think its confidence because this awful streak started right after Indian Wells. She should have been feeling good about that result, but lost early in Miami & Charleston, then kept losing every match since.
This is a long term mess with no easy fix.
Confidence affects stuff like when she nets easy routine backhands that in the past you'd expect her to make 10 times out of 10. Stuff like the serve goes way deeper than that. Even at her best she had things that needed working on (easy shots at the net etc.), but now those things are the least of her problems. Now she doesn't even really have a reliable shot, the backhand use to be one of the best in the game, now it's average by top 10 standards, the down the line is pretty much non-existent. You saw vs Zheng just how problematic her forehand has become, Zheng by no means a big hitter, was finding it easy to hit through Caroline on a very slow court, there is no consistent depth at all from that side.
There is no easy fix because you have a player who is low on confidence and being let down by her strokes. Caro isn't one of these players who can hit out of a slump, there is no keep going for it and eventually it will work because that isn't Caro's game. Caro needs her strokes to be consistent and deep. The problem I see long term is I think there needs to be some technical improvement in order for her to gain her confidence back, but I'm not sure any technical improvement is forthcoming.
You can see right now from on court coaching, Caroline is a mess, she's distracted, letting minor things affect her, it tells you all you need to know about her mental state right now. I don't know how the lack of on court coaching will affect things if at all at Roland Garros, it's clear she is getting down on herself very quickly in matches, but Piotr doesn't seem to be able to get her out of it on court anyway so it may not make much of a difference. You do wonder where it is all currently heading though, you can even see it on here, a number of people's long term optimism is heavily waning right now, and Caro isn't giving off any positive vibes for people to get excited about either.