Yes, it's very clear about its methodology (always a good sign)
I've had a quick look through the ONS charts and I can't see one that does covid deaths by age. So I hope you do return with it, as it might be tucked away somewhere non-obvious and I'd like to see.
The figures (at first glance) between the covid dashboard and the ONS are very little different however. Certainly (IMO) not enough to discredit the trend - especially as for the most part, children weren't tested unless symptomatic (except older children in 2021) and also children generally aren't dying in large numbers from other causes, so the confounder (whilst I agree could have more impact in lower numbers) is very much less likely to occur.