I don’t know about layout, but to add the functionality you just have to change is_visible to is_solo.
row.prop(context.active_object.data.collections["Root"], "is_visible",toggle=True, text="Root")
row.prop(context.active_object.data.collections["Root"], "is_solo",toggle=True, text="Root Solo")
Of course if you wanted to use the icon you could do something like this:
row.prop(context.active_object.data.collections["Root"], "is_visible",toggle=True, text="Root")
if context.active_object.data.collections["Root"].is_solo:
row.prop(context.active_object.data.collections["Root"], "is_solo",toggle=True, text="", icon="SOLO_ON")
else:
row.prop(context.active_object.data.collections["Root"], "is_solo",toggle=True, text="", icon="SOLO_OFF")
