Files shared with Anyone sometimes prompt users to request acccess to the file

I'm working on something similar and found when sharing files directly in SharePoint to a specified user, an e-mail address is added as a parameter in the sharing link. This e-mail parameter creates a LoginHint claim in the auth flow. If the e-mail does not match a user, the user is redirected to the standard sign-in experience. However, if the e-mail does match but the UPN is different, I believe this stops the sign-in flow and prompts to a password. This is still a working theory but may help with your t-shooting processes.