Remove broken surfaces in imported step file

I have imported a step file to Solidworks 2023. It looks like this. 

I want to cnc it via JLCCNC, but got the response: 

The uploaded drawings contains broken surfaces, which makes it unprocessable on our end. We kindly ask you to revise the file on your side to ensure the surfaces are properly closed. [...] On your drawing, there are many lines, which makes it difficult to machine all the details properly, resulting in what we referred to as “broken surfaces.”

But I have no clue how to do this. I already tried a few things:

Import Diagnosis

Import Diagnosis shows no errors, so nothing to fix

Check

  1. Surface - Minimum radius = 0.997 mm
  2. Maximum gap between edges: 0.00390915 mm
  3. Maximum gap between corner points: 0.00390915 mm

Seems not to be the problem for these "many lines", JLC was talking about.

Geometry Analysis

Show many problems, but no way to fix them?

Surfaces -> Remove Surface

This removes the successfully the black lines, but also changes the form of the object completly. No matter which option I select or deselect.

 

I also found this manual, but the fit spline function was not available (greyed out) in my Solidworks. And I have no clue why.  

 

I also installed Power Surfacing, trying this tutorial (https://www.youtube.com/watch?v=cRZ5qhEK5U8), but wasn't successfull either.

 

So does anyone have a clue what my problem is and how to solve it easily? I have 4 different models with similar problems and I do not want to spend hours on each model to fix each line individually...