There is a discrepancy in how the tools’ gizmos are displayed between the toolbar tools and the object gizmos: using the Object Gizmos, with e.g. the Select Tool, keeps the entire gizmo instead of just the axis. I show the example with the Move tool but this is the same also with Rotate and Scale.
Toolbar
Object Gizmos
Can’t really say which one is better, but it would be nice to have the two behaving the same.