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, and why such an adjustment unconventional in this case is necessary, because they are quacks who want to apply arbitrary math to get the outcome they want. As far as I can tell, that means taking people who had dramatically lower death rates after vaccination, and adding the time they spent unvaccinated to the unvaccinated cohort, for no clear reason.

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

I did not read the second paper.