I’m not an expert in this area by any means but it feels like there should be a “motive” angle to this rather just than blanket immunity.

The same actions committed by two different presidents could vary hugely in their motive - one might be legitimately concerned about voter fraud and the other trying to interfere maliciously with election results.

Admittedly the bar would be high to prove malicious intent (eg. acting out of self interest rather than in the interests of the office/country) but that still seems better than just saying that a given action, regardless of motive, is covered by immunity.