The Control Center no longer responds to click events from any script. But the version with the menu bar should still work with a small change.
Try this (I couldn't test it as I don't currently have an iPad):
set iPadName to "iPad"
tell application "System Events"
tell application process "ControlCenter"
repeat with tElement in menu bar items of menu bar 1
if (exists attribute "AXTitle" of tElement) then
if value of attribute "AXTitle" of tElement contains "Display" then
set theBar to tElement
tell theBar
click
end tell
set tElements to entire contents of window 1
set tElements to entire contents of window 1 -- bug in 12.x
repeat with i from 1 to count of tElements
set tElement to item i of tElements
if (title of tElement contains iPadName) then
tell tElement
click
end tell
exit repeat
end if
end repeat
tell theBar
click
end tell
exit repeat
end if
end if
end repeat
end tell
end tell
Note: The menu "Display" (Settings -> Dock & Menu bar -> Display) must be always visible in the menu bar. See: Catalina Sidecar toggle - #23 by Dirk