Bartender 3

This is normally due to misunderstanding Bartender 3's UI i.e. having it reversed, to explain:

By default, when Bartender is running the Bartender bar items are hidden, and the "show in menu bar" and "Always show in menu bar" items are visible, and the Bartender icon appears as ●●●

When you click the Bartender icon the "show in bartender bar menu bar" and "Always show in menu bar" items are shown, and the Bartender icon appears as ○○○

Then with autohides enabled, clicking anywhere else (into another app etc) will cause Bartender to hid the bartender bar items again and go back to its default state, again the Bartender icon would now look like ●●●