If they haven't got them already Ukraine will almost certainly be getting AIM-120Cs and probably AIM-120Ds as for the AA-13 Axehead from what I've read it has not been used to proper effect in Ukraine and an intact unexploded example was found by the Ukrainians in February 2023 and past on to western technical experts for analysis so the ECM gear the new F-16s that Ukraine is getting will almost certainly be calibrated to deal with an AA-13
All of them are 'calibrated' against each other, it's a constant process and I wouldn't read too deep into it; an/alq-213 isn't the most capable ew suit out there either. Those exposures ultimately matter for first week advantage.
If anything, amraam itself (other than D model with it's important - and probably jammable! - datalink) is quite an exposed weapon itself.
AA-13, on the other hand, remains as the most influential a2a missile of the war(a war where fighters are quite secondary beings in the first place), despite that dud.
In regards to those aircraft and the AA-13 I can see the US giving Ukraine a handful of AIM-174Bs to take out those aircraft especially the A-50 (And its' accompanying Il-22M airborne command post) as Russia only has a handful of those aircraft
May as well send them directly to Beijing.
First week advantage doesn't matter to Russia anymore, as it is in a critical conflict; any cool weapon, no matter how advanced, can be countered by organizational answer before any technical reply; R-37m is a perfect example - just time ops in a way to avoid meeting it and carefully control fighter maneuvers - and it's good.
For US, on the other hand,
every single exposure comes at a cost of their first day advantage(s) on their main theatre. Both for them and their allies, who most often don't have money or touch to update compromised solutions fast enough.
Exposing aim-174b (urgent enabler) before there are even proper stocks of them(and provided an/apg-66 can even support such an engagement) - navy will be excited.