You can make a global change to that sharp positioning. Go to Engraving Options/Project Default Appearances/Edit. Enter any chord symbol with a sharp in the root. The chord doesn’t really matter, we just need a way to make a global edit to the positioning of that character. Click the sharp in the editing window, then click the Edit Component pencil underneath which will take you to the Edit Chord Symbol Component window. You can now make a global modification to the sharp positioning. Change the Y value to move it up. You may need to use some trial and error with positioning and switch back and forth between this window and the previous one, but only make alterations in this window. Any modifications in the previous Project Default Appearances window are not global. After hitting Apply, the sharp positioning should now be updated in any chord you haven’t already manually edited.
Just a warning, while consistent with a single character, the Edit Chord Symbol Component editing window is super buggy when positioning multiple characters. Get your sharp position correct first before attempting to modify any of the chord composite characters, because it’s an incredibly frustrating experience.