As IdrisSeabright noted, an .exe file is useless. That's a Windows program/app.
The key is not dead. You can always use your key to install the software, which you couldn't have possibly done yet since you haven't acquired a Mac installer. A download of a Windows version installer is just that. A download. It doesn't count for anything since you haven't attempted to activate the suite with the key yet.
Click on my link above and download the April 11, 202316.72 (23040900) installer. Assuming you didn't purchase the Teams version, it would be the Office suite (without Teams) link. Or, since I just copied the link into my post, you can click this one.
Edit: Heh-heh! You posted again while I was typing. Good to hear you've solved the issue.