This is typical of Covid conspiracy theorists, or conspiracy theorists of any sort: one or two papers on one side prove something, but an overwhelming mountain of evidence on the other side does not prove something. The theorist makes no explanation as to how a planetful of scientists missed the obvious truth that some random dudes found; they just assert that it happened, or make some hand-waving explanation about how an inexplicable planet-wide force of censors is silencing the few unremarkable randos who somehow have the truth.

The first paper seems to claim a very standard cohort study is subject to "immortal time bias", an effect whereby measuring outcomes can seem to change them. The typical example of sampling time bias is that slow-growing cancers are more survivable than fast-growing ones, but also more likely to be measured by a screening, giving a correlation between screening and survivablility. So you get a time effect where more fast-acting cancers do not end up in the measurement, biasing the data.

But in measurements such that one outcome or the other does not bias the odds of that outcome being sampled, there can be no measurement time effect, which is why it's not corrected for in studies like this. The authors do not explain why measurement time effects would have anything to do with detecting or not detecting death rates in the abstract, or anywhere else in the paper, because they are quacks, who apply arbitrary math to get the outcome they want.

As another commenter pointed out, randomized controlled trials -- which cannot possibly have this made-up time effect -- often clearly show a strongly positive effect for vaccination.

I did not read the second paper.

There is no conspiracy, the studies were all crap! They raced through them and failed at basic double blind experiments as well as giving control groups live shots afterwards, thus eliminating any retrospective studies. There was never any positive effect. It didn't exist. It's disgusting what happened and how so many professionals that we rely on to stand up and tell the truth knuckled under to the pressure of the moment and lied or turned their backs.