According to official notice by apple
X11 is no longer included with Mac, but X11 server and client libraries are available from the XQuartz project.
why X11 matters in this case ?
xdotool - command-line X11 automation tool.
So Alongside setting export DISPLAY=:0
install xquartz.
What does DISPLAY means exactly?
according x manual
From the user's perspective, every X server has a display name of the form:
hostname:displaynumber.screennumber
This information is used by the application to determine how it should connect to the server and which screen it should use by default (on displays with multiple monitors):
hostname The hostname specifies the name of the machine to which the display is physically connected. If the hostname is not given, the most efficient way of communicating to a server on the same machine will be used.
displaynumber The phrase "display" is usually used to refer to collection of monitors that share a common keyboard and pointer (mouse, tablet, etc.). Most workstations tend to only have one keyboard, and therefore, only one display. Larger, multi-user systems, however, frequently have several displays so that more than one person can be doing graphics work at once. To avoid confusion, each display on a machine is assigned a display number (beginning at 0) when the X server for that display is started. The display number must always be given in a display name.
screennumber Some displays share a single keyboard and pointer among two or more monitors. Since each monitor has its own set of windows, each screen is assigned a screen number (beginning at 0) when the X server for that display is started. If the screen number is not given, screen 0 will be used.
there is simpler description found here
A display consists (simplified) of:
- a keyboard
- a mouse
- a screen
i.e. when you connect over ssh you are using different sets of these 3.
xdotoolis an automation tool for the X11 window system. macOS doesn't use X11 - although it can be installed, it is unlikely to give the results you are looking for. This seems like an XY problem - what exactly is the issue you're trying to solve with xdotool?DISPLAYis in X11