Dear @Byron Schaffer,
I can understand how frustrating it is when essential features like the "Share" button fail to load, especially after you have already put so much effort into troubleshooting. Since the issue follows the user across multiple devices but works in the web version, the problem likely lies in the interaction between the user's identity profile and the Office service.
Based on the steps you have already taken, I recommend trying these specific solutions to resolve the "Loading" loop:
Step 1: Reset the Office Sign-in State (Clear Identity Registry)
Sometimes, persistent identity fragments in the Registry cause the "Share" UI to hang.
- Close all Office apps.
- Navigate to:
HKEY_CURRENT_USER\Software\Microsoft\Office\16.0\Common\Identity 
- Right-click the Identity folder and select Export (as a backup).
- Then, delete the Identity folder.
- Restart Word and sign in again. This forces a fresh handshake with the sharing service.
Step 2: Check for "Optional Diagnostic Data" Settings
The Share window is a modern "Web View" component. If certain privacy settings are too restrictive, it can block the window from loading.
- In Word, go to File > Account > Account Privacy > Manage Settings.
- Ensure that "Enable optional connected experiences" is checked. If this is disabled by an IT policy (GPO), the Share dialog may fail to initialize.

Step 3: Verify OneDrive/SharePoint Service Connection
Even if the user can access files, the "Share" service specifically relies on a connected service entry.
- Go to File > Account.
- In the Connected Services section, check if OneDrive or SharePoint is listed. If it is, click Remove service and then Add service to re-link it (removing is only possible if you have connected both OneDrive personal and business).

We have previously seen incidents were OneDrive integration causes Office apps to become unresponsive. I recommend checking the Microsoft 365 Service Health Dashboard for any active advisories related to "Share Dialog" or "Office Web Components."
If these steps do not resolve the issue, it may be necessary to recreate the user's M365 profile from the admin side, as there could be an underlying corruption in the user's object in Entra ID (formerly Azure AD).
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