Yes, the push event does not have optional activity types.
You can use the path filters to configure a workflow to run only when there is any modified file can match the patterns you specified.
Any file that is added, updated or deleted in the pushed commits can let the push event trigger the workflow.
If you really need the push event can support some activity types, I recommend that you can directly share a feature request in the Feedback form for GitHub.
That will allow you to directly interact with the appropriate engineering team, and make it more convenient for the engineering team to collect and categorize your suggestions.