Those are really valid points, thank you.

I think point 1 is a valid finding of their study because it doesn't violate the assumption of self-control case series design that the outcome of interest in period A must not affect the same in period B. Specifically, people who did not die in period A (28 days post-vaccination; risk period) can still be included in the denominator of period B (25 weeks post-vaccination; baseline period), but this can't be done with deaths.

And unfortunately, I'm not aware of any study that has compared thoroughly compared the risk-to-benefit ratio of booster shots, taking into account the possibility of reinfection after vaccination and all other factors.