This is an accepted solution.
Rae from Shopify here.
I appreciate you reaching out about the search icon on your Venture theme, and sharing your store's URL.
On the mobile version of Venture, the search bar will show up within the sidebar menu, rather than in the top righthand corner of the page, like it does on desktop view.
With that in mind, when you visit your site on mobile view, does the search bar appear in the top lefthand corner when you open up your main menu? It should look similar to this:
If the search bar isn't showing up here on your theme, can you please confirm if you've made any coding changes that might have impacted this?
Equally, if you would like to discuss moving the search function on mobile view, I recommend speaking with our Support team about this directly. That way, our team can verify your account, and double check if the changes you're looking for are possible. To get started with this, please visit our Help Center, log in to your account, and create a support request with us there. Once we receive your request, we can help further with this via email, live chat, or through a callback.
Since this information outlines exactly how to find the search bar on the Venture theme, and make potential changes to its location, I've marked my reply as a solution to your thread. This should help other merchants who are also looking for more details on this.