I think it's hard to demonstrate any significant changes in all-cause mortality, considering that participants enrolled in Pfizer's vaccine clinical trial are mostly healthy adults or adults with stable medical conditions.
It's unfortunate that the report didn't provide any info on the statistical analysis of all-cause mortality. The 4 excess deaths per 20,000 vaccinated people can be a signal, but I honestly don't know. The report doesn't seem to disclose what those deaths were.
That said, I'm aware of one large-scale surveillance study from the CDC that found lower risks of non-COVID-related deaths in vaccinated than unvaccinated people. If Covid deaths are included, I imagine the all-cause mortality would be lower in vaccinated than unvaccinated people.
