Start menu "Best Match" allowing access to run command

We operate an educational network of PCs which we restrict quite strictly to prevent students accessing certain programs. We use a number of group policy settings already to restrict the command prompt, hide or restrict certain drives and prevent access to the run command (via right click on start button and within the start menu). However, the recent updates to the start menu in Windows 11 allow users to search (and run) applications and network UNC paths, which they previously wouldn't have access to. We have found that the "Best Match" on the start menu search, allows users to open UNC paths to servers which are normally blocked by group policy when keying in to the address bar in explorer. Disabling the run command has always been effective at preventing apps being run which we don't directly present in the past. This creates a bit of a vulnerability for us as we need to run as tight a setup as possible to prevent students tampering. We need students to be able to write to shares, but we don't want them to be able to browse directly to the root of server shares (even if the permissions are tight around the shares).

The only way we've found to prevent access to this is to fully disable the search UI. As this policy is a computer policy we cannot disable this for only certain users which is frustrating. The DisableSearchBoxSuggestions setting has no effect on the "Best Match" suggestion.

We feel that Microsoft need to address this issue, as being able to prevent access to the "run" command is important to many Network Admins in Education.