The Archer Card still being intact is because Miyu is abusing the Counter Force's corrective history again. It was destroyed in the original timeline, but the new timeline consisted of Miyu using Archer Install to shoot down Julian-Darius -- he never got the chance to destroy the Archer Card here. (This is shown in Chapter 67.)That card was destroyed though, which is why Kuro is "dead". So I am not sure where Miyu yanked it from. I don't believe it's Gilgamesh's card, Kid Gil took off with that one and he hasn't come back yet, unless I missed something.
That archer card is also actually not an "Archer" card at all. It's a fake "Nameless" card that is later imprinted with Emiya due to it's connection with Miyu's Shirou. I'm not entirely sure of the mechanics, but one thing that is clear is Kuro had this card permanently installed, or rather she was using it as a body. Meaning it might just be an empty "Nameless" card again, except for it being a catalyst.
If an archer is summoned, it would make more sense that Gilgamesh is summoned. The actual archer card of the Ainsworth HGW is his. The fact that Gil is already summoned, or that he's holding onto his card, are all probable reasons why the Archer is missing.
Also worth noting is that Archer Miyu had an Emiya-adjacent outfit and bow under Archer Install, so the Archer Card is definitely still Emiya. Which begs the question why Emiya wasn't summoned along with the rest...
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