Outlook Not Able to Open Files in Desktop App

Your own tests narrow it down well: it works in Outlook web, in classic Outlook, and when the file is downloaded first, but fails when New Outlook hands the attachment to the desktop app. So the files and the Office apps are fine, and what is breaking is the hand-off, where New Outlook saves a temporary copy and asks Windows to open it. Silent failures there are usually caused by something that blocks the launch or the temporary copy. I would check, in this order:

• Security software. Defender attack surface reduction rules, Controlled folder access, or a third party EDR can block the launch of Office or Acrobat from a process that came from an email, and they do it without showing an error. Look in Event Viewer > Applications and Services Logs > Microsoft > Windows > Windows Defender > Operational (events 1121 and 1122 for ASR, 1123 and 1124 for controlled folder access), and check your EDR's block log at the time of a failed attempt.
• What the two affected machines have in common. Compare them against a machine that works: New Outlook version (Settings > About in the app), Windows build, WebView2 runtime version, and the Office update channel. Two cases in an enterprise often turn out to share the same recent update or the same policy.
• Repair the app. Settings > Apps > Installed apps > Outlook (new) > Advanced options > Repair, then Reset if repair does not help. A cleared local cache (the Olk folder under %LocalAppData%\Microsoft) sometimes fixes a broken hand-off.
• File associations and the temp location. Check that the default app for .docx, .xlsx and .pdf is set normally, and that the folder New Outlook uses for temporary files is not redirected, blocked by policy or full. A Group Policy or Intune setting that affects Attachment Manager, Protected View for attachments, or the file zone information can also change the behavior.
• Capture it. Run Process Monitor while you click the attachment and filter by olk.exe, and you will see whether it writes the temp file and where the launch is denied.

If the two cases line up with a new New Outlook build, report it through the Outlook feedback option with the version numbers, because it will be hard for the product team to reproduce without them.