Long story short, in Adobe Illustrator to prepare file for print the right way I just had to use Select Objects — Stroke, Convert to Outlines, and that's all.
In Designer it seems I have to select manually all strokes and try Expand Stroke / Convert to Outlines a few times, praying they will do something. Even if Convert to Curves works, it just randomly erases part of graphics with no possibility to undo these steps, thus corrupting the whole source file. To prepare a simple file, it took me 10 minutes working with duplicated backup file, instead of 10 secs.
Video and sample file attached, you can try convert those icons to curves 😂
I don't need any suggestions regarding this issue (have to use Illustrator for pre-press), just fix this.
Screen Recording 2022-12-05 at 10.44.32.mov
Corrupted file for Affinity.afdesign