What a great idea for a Shop! I really enjoyed taking a look at your store and thank you for sharing that link and explaining the issue. I am sorry to hear you are having problems with your menu when viewing the store via mobile devices. I was not able to access your menu through mobile when I tested it out on my end as well.
Moving forward, there are some suggestions I can offer for you to look into this issue further. Are you utilizing a Shopify theme or a third-party theme, and have you recently made any coding changes to your store?
Something else to consider would be third-party applications. Have you recently added or deleted any third-party apps that affected your products or storefront in any way? If so, the deletion of that specific app could have left some residual coding behind causing issues.
A good way to test if an issue is theme-specific is to check a fresh Shopify theme in your admin's Theme library.
If you try this and your menu is working as intended in the fresh theme, when you switch to your mobile view, this would point to an issue specific to your primary theme.
I also noticed that on your desktop view, I could not access your Shop menu item. When clicking "Shop" I was not redirected to any specific products or collections, is this intended?
If not, I recommend heading to your admin and clicking Online store and Navatigaton to ensure you have the correct link set up under your "Shop" menu option. This will ensure your customers are re-directed to the products you intend to showcase under that "Shop" menu item.
Feel free to reach back out here once you try the above steps with any further context in regards to, recent apps added or deleted as well as the name of the Theme you are using. Depending on the Theme, there may be a couple of alternative suggestions I can offer you to get this looked into!