Screen opacity doesn't work

Thank for all the answers. I made it in RGB mode and it worked. 🙂

I just tend to avoid all blend modes other than Multiply and Darken. Blend modes, really just change colors, that's all - sure they can be a quick, easy, way to change colors, especially for multiple objects - nonetheless, that's all they do.

You can create the same effect in CMYK file by merely using a color to transparent gradient with a "Normal" blend mode, rather than a white to transparent gradient set to "Screen".

You could try if this works for you:

Create the objects with the screen effect in an RGB document.

Select them together with the background and choose: Object > Flatten Transparency with a High Ressolution preset.

Copy and paste the result in a CMYK document.

It may be useful to keep an unflattened copy of the RGB version, the flattened one will be partially uneditable.