Adobe Apple Silicon – How Current Adobe Products Run on New Macs

You can use Activity Monitor to view all the processes running on your Mac at any time. If you prefer to use the terminal, you can use top.

Here's a piece of code that just gets desktop's dimensions and transfers them to another application's first window.
Exchange "TextEdit" with Illustrator's process name and build yourself a Service in Automator (open "New", choose Service, draw "Do AppleScript" to right, insert this code ...).
Give it a shortcut via [ System Preferences > Keyboard > Shortcuts > Services ] and get going!
Hope this helps ...

tell application "Finder" to set myBounds to bounds of window of desktop

tell application "System Events" to tell process "TextEdit"
    set position of window 1 to {0, 20}
    set size of window 1 to {item 3 of myBounds, (item 4 of myBounds) - 20}
end tell