FormStyle property "fsStayOnTop" means that form will stay on top of other forms in the same application.
If you want your form to stay on top globally, then you should set it to "fsSystemStayOnTop".
In
Lazarus_0.9.30_release_notes article, you can find this:
TCustomForm.FormStyle added fsSystemStayOnTop.Meaning is same as with fsStayOnTop except that fsStayOnTop is form on app top, so when application deactivates fsStayOnTop is not on top of other application(s), fsSystemStayOnTop is always on top.