I agree the archway is a metaphor for death, the sudden and irreversible nature of Sirius' death reflects this, I think.
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Just before he goes through the beg archway, Sirius is hit by a spell, so could have been dead before he goes through the veil. It's a neat way of not having a body, a funeral or any closure for Harry. Bellatrix is both to blame and not to blame, and you can see this in both Harry's searching for a villain in Snape, and also in that he later tries to use crucio on her because he hates. (Although at that point he doesn't quite manage it as 'You've got to really mean it". That tells me Harry is still blaming others, himself, Snape and Dumbledore for Sirius' death in book 6. By book 7 he refers to it as the wand that kills Sirius so I believe that's him coming to terms with his own guilt and what happened to Sirius. It also implies to me that she was more culpable than him simply falling through the veil.
The veil itself follows in the footsteps of veils as gateways to the other world/unknown across literature and myth. I don't think that's an accident because JK is well read and into symbols and origins. Romantic poets, classic literature etc. The hearing whispering and yet not seeing, being unreachable reflects death very accurately as well. Having Luna, who has experienced loss and is open to the supernatural being the other character who hears the voices is a nice touch too.
I find Sirius death really hard to cope with because of all the reasons above. As I said above, it's a lot more real and raw than Cedric's death in the books. Harry is somewhat removed from Mr and Mrs Diggory's grief in the books as they are numb and he doesn't see all the stages of grief. With Sirius he very much experiences all the stages of grief himself, with the added burdens of guilt and no closure. If it were a Mumsnet thread it would come with a trigger warning!