1Password menu bar doesn't open immediately when using Bartender

When using https://www.macbartender.com's Bartender Bar, 1Password's menu bar menu doesn't show immediately and only after clicking it once it is no longer hidden and is part of the regular menu bar, it opens. This makes it harder to open the menu quicker, both from clicking the icon and from using Quick Search. I haven't seen any other menu bar item with this behaviour.

Steps to reproduce

1. Move 1Password's icon to Bartender's "Hidden menu bar items"
2. Trigger the Bartender Bar
3. Click the 1Password logo
4. Notice the menu (with "Open 1Password") doesn't show up
5. Click the 1Password logo again, from the menu bar icon that is now unhidden
6. Notice the menu shows up
7. Wait for the 1Password menu bar item to hide again
8. Open Bartender's quick search
9. Search and open 1Password
10. Notice the 1Password menu bar item is unhidden but the menu is not opened
11. While the 1Password menu bar item is still unhidden, quick search 1Password again and open it
12. Notice the menu is shown
13. Quick search another hidden application's menu bar item and notice it is unhidden and the menu is shown at the same time without having to search for it twice

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1Password Version: 8.8.0-156 BETA
Bartender Version: 4.2.0
OS Version: macOS 12.4