I'm in no rush.
They are otherwise up to date including this year's flu spray, but the gains for 12-15 were pretty marginal according to the JCVI, I can't see it being better for 5-11.
We've had a lot of Covid through school since October, so they've already been exposed, and most children we know have either tested due to a minor "cold" or assymptomatically through contacts. At this point, I'm not convinced that the medical benefits are for the majority of healthy children.
Both AZ1 and the Moderna booster have given me unpleasant (but minor) side effects, more than any other vaccinations I've ever had. (The only other preventative medication I've had worse was for malria to the point that I couldn't keep it in.) The vaccines have disrupted me more than cold-like symptoms do. Not something I'd be excited to replicate for my children.
My concern is that we'll be forced into a political decision, not a medical one. We have family abroad and between travel/ carehome restrictions, it's over 2 years since the DCs have seen their granny. Indeed they've not seen a relative over 60 since the end of 2019. They've lost 6.5+m of education, a vast swathe of family life, social skills, so many development opportunities and they owe strangers absolutely nothing. The other coercion point is if like adults, it affects self isolation protocol.
TBH getting a booster to get through this winter is one thing, but I am really, really not enthused by a potential prospect of constant vaccines to participate in normal life.