Apple Script - How do I check if a window with a specific title exists?

You can do this with the System Events application - for example:

tell application "System Events"
    if exists (window "Terminal — -zsh" of process "Terminal") then
        display dialog "Found"
    else
        display dialog "Not found"
    end if
end tell

Note that process is case sensitive while window is not. Therefore this will work

if exists (window "TeRmInAl — -ZsH" of process "Terminal")

but this will not

if exists (window "Terminal — -zsh" of process "terminal")

If you are running from Script Editor you must authorise it in System Preferences > Security & Privacy > Privacy > Accessibility

Yes, it is simple and there is no need, in this case, to involve System Events. Just ask Notes directly if the window exists, e.g.:

tell application "Notes"
    exists window "Notes"
end tell

This returns either true or false, however the code in this form may not be as useful as either wrapping the query in an if statement block or assigning the results to a variable, e.g.:

tell application "Notes"
    if exists window "Notes" then
        # Do something.
    else
        # Do something else.
    end if
end tell

Or:

tell application "Notes"
    set itExists to exists window "Notes"
    if itExists then
        # Do something.
    else
        # Do something else.
    end if
end tell