kinda weird for you to cite someone else's work when you report those numbers then no?

No, you can use the info there and elsewhere to do your own risk calculus. They have their raw counts in the table.

First, are you using "significantly" here to mean statistically significant or as a synonym for "much"

Both depending on your alpha level; the odds ratio for this specific dataset and viral myocarditis is

  Fisher's Exact Test for Count Data

data:  matrix(c(3, 12460 - 3, 18, 284592 - 18), ncol = 2)
p-value = 0.05583
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
  0.7182998 13.0456836
sample estimates:
odds ratio 
  3.807808 

That's a pretty large effect size in the sample.

Without more information about how much uncertainty there is in these odds, even if we abuse the statistics to draw an invalid comparison, at best we'd conclude that the post exposure odds of dysautonomia are about the same between groups.

There is no abuse of statistics or invalid comparison to report an observed sample difference. Sample proportions are unbiased estimators. They observed an higher IRR in the post-vaccine than the post-infection group. It'd be inappropriate to claim with any level of confidence maps to the population proportions, but nobody is doing that.

You seem to have at least a passing knowledge of probability theory, so please, reread the authors' corrections for their own explanation as to why the comparison that your argument rests on cannot be drawn from the data or results in the work you cited, for POTS, myocarditis, or any of the other outcomes studied.

I'm a statistics professor. Their note on fully adjusted odds comparisons isn't of interest to me doing back of the envelope math for my own personal risk calculations. Unless you're going to posit the the presence of severe confounding factors between the two seperate populations, I'm going to help myself to the null that the randomization limits the effect of the populations being exclusive on the final parameter in question. They helped themselves when they did their between group comparison, and you felt it was worth including and bolding when it supported your argument.

these results indicate that POTS might be occurring at a higher-than-expected frequency following COVID-19 vaccination, although at an overall rate lower than the frequency of POTS occurring following SARS-CoV-2 infection.

You kinda do if vaccination unconditionally lowers the risk of negative outcomes,

Why would you ever use unconditional probabilities for inference when the prevalence of negative outcomes are so heavily stratified? To give you a more extreme example, this is like quoting airplane safety statistics at someone whose on a plane that the wing just fell off of. The statistics about unconditioned airplane safety are true, but meaningless once conditioned with additional information. Specifically, the study you linked to on myocarditis found a large effect with the Moderna vaccine than they did with covid infection.

In the studies that have included mRNA vaccine and SARS-COVID-19 myocarditis measured by the same methodology, the incidence rate was increased by 3.5-fold over control in COVID-19 compared with 1.5-fold for BNT162b2 and 6.2-fold for mRNA-1273.

When you know which vaccine someone got, the appropriate probability is the conditioned one, not the unconditioned one.

To sum up this digression into statistics, if you can estimate the odds ratio of negative outcomes to infection and vaccine (for a specific cause or all cause, that's your choice), conditioned to your specific demographic and health information, you can then calculate a daily risk of COVID infection, p_critical, at which point rolling the dice with covid is actually a safer bet than the vaccine. That might be quite small, and very likely will be for most people, (to the point where the vaccine is a safer bet), but it's not 0. To give you a concrete example; my 95 year old neighbor is unvaccinated. She hasn't been to an indoord public place since February 2020, apart from doctors offices, which she wears an n95 into. She only has me and her daughter come into her house, and everyone will wear an n95. She has a list of drug sensitivities and comorbidities as long as my arm (I do grant that I consider some of these exaggerated). Her daily risk of infection is so vanishingly low, that yeah, in her case, p_infection< p_critical, the probability likely works out in favor of not vaccinating. Do you buy that?

That's an opinion you should keep to yourself in a post explicitly created to vent about someone in OP's life deliberately doing less less than OP has asked for to protect themselves and OP.

Only if we want them to stay mad at their significant other. He's welcome to be mad about his situation, he should be. But what good outcome do you foresee about reinforcing that anger at an individual and not the fucked up system that put us here.