saved search -> saved
 

Where is "saved Search"saved so that I can also transfer these "searches" to other computers with Calibre?
When copying the configuration directory nothing changes in "saved search"

They are in the library, which if you think about it, makes sense. You'll see them in the ../<library>/metadata_db_prefs_backup.json file. Library preferences can't be transferred independently of the library itself.

BR

Or use a workaround:
On the computer with Calibre and the existing search: In Calibre, click on "saved searches", select "manage saved searches", select the search you want and click "edit search". Now, copy the search data themselves to Notepad, or another text editor. Save this notepad file to your computer. Copy this text file to your other computer. And now you can import your search data into the new calibre library: On the new computer, click on "saved search", click "manage saved searches", click "add search", and here you can add the name of the search, and the search data from the text file. Click on ok, and then again on ok. Now you are set to go with your search.
If you keep that text file on a usb stick, you can at all times move the searches you want to other computers where ever they are and need these searches.