As per the documentation regarding Upload a New Version of a File, the note section says that
Only file owners, collaborators, and users with the Modify All Data permission can upload new versions of a file.
When we enable Modify All Data, this doc points out to all the permissions that will be enabled as soon as Modify All Data is enabled - https://help.salesforce.com/s/articleView?id=000384401&type=1
Is there an alternative (possibly a lower level permission) targeted just for the functionality, that takes care of uploading a new version of a file in Salesforce ?