[Question] What do we know about vaccinating children?

In Germany, the BioNTech vaccine has been approved for children:

At the end of May, the Comirnaty mRNA vaccine developed by BioNTech /​ Pfizer was approved by the European Medicines Agency (EMA) as the first COVID-19 vaccine in this age group for children and adolescents aged 12 and over. -- Robert Koch Institute

But it is still not generally recommended for this age group:

There is currently no general vaccination recommendation of the STIKO for children and adolescents from 12 to 17
Years, but only for children and teens with a specific risk. -- STIKO informational material Robert Koch Institute

I have four generally healthy boys aged 10 to 17. Only the oldest is already vaccinated, being basically an adult. I am inclined to get them all vaccinated with BioNTech because the risk-benefit tradeoff with such a safe vaccine seems obvious.

For a cautious view of the risks, see e.g. this LessWong post:

conditional on a kid catching COVID, … a ~2% chance of a miserable months-long ordeal until they recover, plus (overlapping) ~1% chance of a big-deal long-term latent problem … -- Young kids catching COVID: how much to worry?

Nature has an article about the general topic:

Thus far, the vaccines seem to be safe in adolescents1… A potential link between the Pfizer vaccine and heart inflammation … the risk of these conditions is … about 67 cases per million second doses in adolescent males aged 12–17, and 9 per million in adolescent females in the same age group. -- Should children get COVID vaccines? What the science says

So my question is: What else do we know about the risk-benefit trade-off of vaccines for children? When and based on what criteria should children get vaccinated? What other considerations should be taken into account (the nature article mentioned fairness, for example)?