I'm talking about the same, and I'm working on the assumption that they may be similar enough for the same reasoning to continue to apply. When we're talking about a variant of the same virus, it would seem unwise to simply assume the opposite. The presumption should, generally, be that the potential for the risk is similar; if we wait for further data, particularly for data on conditions that can take a while to develop, very substantial numbers of people will have already been exposed to the potential risk at that point.
In terms of the vaccine's effectiveness against infection, I said it
reduces the risk, not prevents. And it can still substantially do that;
UK vaccine surveillance (pdf) indicates that with Omicron, 2 doses of Pfizer or Moderna has 65-70% effectiveness waning to 10% by 20 weeks after the second dose, and after a booster dose, from 65-75% effectiveness dropping to 55 to 65% by 5-9 weeks and to 45-50% from 10+ weeks.
Bearing in mind that the risk of severe effects from illness is a combination of the risk of infection and the risk of severe effects if infected, even that reduced level of effectiveness against infection is significant.
I'd add that the data also indicates that the vaccine effectiveness against hospitalisation is also substantially higher after second doses and boosters ("When combined with vaccine effectiveness against symptomatic disease this was equivalent to vaccine effectiveness against hospitalisation of 58% after 1 dose, 64% 2-24 weeks after dose 2, 44% 25+ weeks after dose 2, and 92% dropping to 83% 10+ weeks after a booster dose", from the previously linked report). That's in terms of the general population, so the impact of that will vary with base levels of risk, but the relative difference is likely to still be present across the age demographics.
I do find it generally odd to consider the risk of death or severe illness in children from Covid to be 'close to non-existent', while regarding the
lower risk of typically mild myocarditis from vaccination to be more significant. From my point of view, vaccination in children represents an overall reduction in risk, and while that is, relatively a low to very low risk to start off with, depending on whether you're considering risk of long-term effects such as long Covid, risk of hospitalisation, or mortality, especially in the case of the latter it's a very low risk of potentially very high consequence. So I would still see it worthwhile to further lower that risk through vaccination, and overall, taking everything into account (risk of severe illness, mortality, and long Covid) speaking of children generally, I can't personally see how the balance swings any way other than towards vaccination.
It's certainly true to say it's less significant a difference in children than it is in the older population, where the reduction in risk is a reduction of a much more substantial risk, but it's still a reduction in risk nevertheless.
But having said all that, in that specific instance rather than generally, I definitely wouldn't vaccinate him 3 days after infection; I think generally the advice is to wait 12 weeks after recovery in the first place. And family history of particular conditions takes the consideration out of the general case, which could swing either way, depending on whether it's considered to present an increased risk from Covid more so than from vaccination, or vice versa.