The problem is that 25% lower risk of all-cause mortality is too big to be explained solely by the vaccine. The reduction is similar when excluding deaths due to COVID-19, and is probably driven by people who got the vaccine being different in some ways that the observational study isn’t controlling for.

Yeah, but there's a plausible explanation for this: Likely, people who get vaccinated also are more likely to do other things to improve their health.

Could it mean that lots of Covid deaths are being attributed to other things?

If you don't get the covid vaccine you probably do other risky things. Not get other vaccines, don't see the doctor about various issues...