The shell context menu including custom items by shell extensions is supported, of course.
However, you cannot have items of 64-bit shell extensions in the shell context menu of a 32-bit application and vice versa. This the law by Windows architecture.
Workaround: Often this can be fixed by installing the 32-bit version of the application "side-by-side" with the 64-bit version.
Thank-you for your reply. By "the application", do you mean XYplorer, or the other application I want to use with it (for example, 7-zip)? If the latter, that could lead to a lot of extra installations.