The shopping cart is probably not there because notification has been set. Normally the third point in the admin area is shop management, see screenshot

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Hi Daniel, delete notifications doesn't help :(

attached pic without notifications 

Which version of WebSite X5?

E-commerce shopping in Control Panel in Pro version only, see

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WebSite X5 online Control Panel

WebSite X5 automatically sets up an online Control Panel for each website created with the Program. It is used by Site Administrators to: 

• display website hit (visits) statistics;
• handle comments on posts in the Blog or comments for the Comments and Ratings Object;
• display Dynamic Content Objects;
• display the users who have registered to access Members' Areas;
• handle orders in the e-commerce shopping cart and check stock availability levels.
• manage the comments the customer leave for the products of the online shop.
• activate and manage push notifications to stay constantly up-to-date about what happens on your website.

>> https://guide.websitex5.com/en/support/solutions/articles/44000618332?utm_source=software&utm_medium=Pro_2023.3

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yes I have PRO version 2023.3.5

If the Pro version is used, then perhaps reinstall WebSiteX5 or wait for the moderators or Incomedia employees (during office hours in Italy).

Why is the shop only half displayed on desktop computers?

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Not sure , i dont see the problem , what size of your screen ?

My notebook - display 1600x900 

Firefox = half width

Edge and Chrome = full width

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If you upload a new shop template with products to the web space and access the admin area, you will not see an “Online Shop: Shopping Cart”.

So WebSiteX5 decides whether the item “Online Shop: Shopping Cart” is displayed in the admin area or not, but I don’t know what requirements have to be met for this to happen.