How to get the display button on the menu bar?

You can only get a mirroring options in the menu extras bar when they are available. That setting is at the bottom of the Displays preference. There is no menu extra item from Apple that will offer any other Displays selection such as resolution, or monitor selection.

There may be a third-party solution in the Mac App Store.

As a small addition to what VikingOSX wrote, while there is no menubarlet to change display settings per se, there is at least one (well, make that two) very quick shortcut to open the Display pane of System Preferences: Option-F2 (actually Option-F1also works). It is quite mnemonic since F1 and F2 are the display brightness keys.

[Bonus: can you guess a shortcut to open the Sound pane? Hint: there three of them :-)

There also two shortcuts to open Keyboard, and one to open the Mission Control pane of System Preferences.]

Additionally, you can get a full list of available menu bar icons by going to Finder > Go > Go to folder and type in:

/System/Library/CoreServices/Menu Extras

It will show you the complete list. If you want one, just double click it and it will appear in the menu bar.

FWIW, you might want to try SwitchResX. https://www.madrau.com/

Once the free trial is over it still functions with certain features disabled. It's only $16 to purchase. Depending on your needs it may be worth looking at.

That's cool! I did not know this one. Thanks!

I’ve had that in my “cool - keep” folder for a very long time....