There are no studies which have found statistically significant links between political measures and excess COVID deaths.
From the conclusions section:
“Regarding government's actions (i.e., containment and stringency index), no association was found with the outcome, suggesting that the other studied factors were more important in the Covid-19 mortality than political measures implemented to fight the virus, except for the economic support index.”
One difference with those is that their governance and infrastructure to tackle a pandemic already existed, which counts. You could write that off to existing 'public health', as you have tried to stretch from the paper, but that is a disingenuous of that research.
A quick search implies that you are also not looking very hard to find studies that don't find linkages. "The results presented in this paper suggest that policy interventions may well explain the majority of cross-country variation in officially reported Covid-19 deaths."
https://link.springer.com/article/10.1007/s10640-020-00466-5
Since we’re not there yet, let’s wait and see.