Thank you for your answer. I would like to have some customization, main things would be
1) Password protect the page
2) Remove some menu line that is present by default and that I can usually edit away in the “Page Editor”
3) Put a title bar with background etc.
All that is not editable when the shop page is set as “main shop page” in the woocommerce options.
The only solution I found to date is to put “no page” as a “main shop page” in the woocommerce options. But then I have some permalinks problems, like the “empty cart” back to shop permalink not perfectly working.