Windows – Run a batch file when I lock/unlock the computer

You can accomplish this by using forfiles.

Forfiles can search for files, and then execute a command and use the files it finds as a variable, or do some checks. Forfiles supports filemasks, and given that you explained that the exefile is the only file in the folder, forfiles can be used.

Your script would look like this:

echo Downloading file...
start "" https://TheWebPagesName.com
PING localhost -n 10 >NUL
echo Running file...

:: comment out old row for easy reading    
:: start "C:\Users\MyUsername\OneDrive\Dokumenter\Foldername\*.exe"

:: insert new comamnd instead:
forfiles /p "C:\Users\MyUsername\OneDrive\Dokumenter\Foldername" /m *.exe /c "@file"

:: if you were not using executables, but would want to use start file.txt, you would use:
::forfiles /p "C:\Users\MyUsername\OneDrive\Dokumenter\Foldername" /m *.txt /c "cmd /c @file"

PING localhost -n 10 >NUL
echo Deleting File...
del "C:\Users\MyUsername\OneDrive\Dokumenter\Foldername\*.exe"
PING localhost -n 2 >NUL
echo Done!
PING localhost -n 6 >NUL
echo Exiting...
PING localhost -n 4 >NUL