AppleScript/Finder not finding the Numbers application

This fragment of a script does a simple check for the existence of Numbers in the Applications folder:

tell application "Finder"
  set AppFolder to folder "Applications" in startup disk as string
  set NumApp to AppFolder & "Numbers"
  set NumExists to (exists NumApp)
end tell

But it doesn't find it. Numbers does exist:

vger:~(128)+>- ls -dl /Applications/Numbers.app/
drwxr-xr-x@ 3 root  wheel  96 18 Sep 13:33 /Applications/Numbers.app/
vger:~(129)+>-

So why does Finder/AppleScript think it doesn't?

This happens on macOS 14.x and 15.x.

Combining the suggestions of @wch1pink, @Mockman and @Ted Wrigley here are two approaches:

set AppFolder to path to applications folder
set NumLoc to AppFolder & "Numbers.app" as string

try
    NumLoc as alias
    set NumExists to true
on error
    set NumExists to false
end try

The setting of the variable is just for illustration. Or more directly:

if exists application "Numbers" then
    set NumExists to true
else
    set NumExists to false
end if