My files from external hard drive will be immediately deleted

I do and did the same on both discs.

Without knowing why, it now works the normal way now with both discs. I had to do a forced new start and I also used the hard disc in question with another Macbook with an older operating system where it worked and then it worked also on the new one.

Thanks for your suggestions

Thank you for your suggestions.

In my finder settings both items you emphasised with a red frame are marked.

I did what you wanted me to do and nothing changed. There must be another reason as the USB-stick behaves in a different way as the external hard disk.