Yes, I'd absolutely listen to the vet on this. And yes, this might explain some of the subtle changes you've been noticing. You'd be pretty uncomfortable too if you couldn't pass waste. This is something you should routinely & very gently feel around for above your snake's vent (& higher up ventrally, for any odd lumps & bumps) particularly if you think something may be wrong. Not to make a big thing of it, but when you're handling- pay attention.
Urate stones are not that rare (you never notice them if they're small enough for the snake to expel normally) but sometimes a snake will form a urate "stone" that's just too large to expel without help. I don't think it has much to do with feeding 2 rats at the same meal, although that's inadvisable anyway for other reasons. (And rats have very thick fur that's hard to digest, which if combined with some dehydration, could promote constipation- though it's not common.)
Snakes are fed all the time before they defecate from the most recent meal- there's nothing unusual about that. (Are you really trying to blame the forum for your snake's problem?) Many years ago, I had an old rattlesnake (given to me very late in her life- she was a "zoo surplus" animal) that formed several "stones" (aka "cloacaliths") which she needed help to pass- she was just fine after that. You want to make extra sure to keep this snake well hydrated in the future, but hopefully this is just a one-time thing. Also, more activity on your snake's part helps to "keep things moving"- another reason to add enrichment to her home- plus, more activity promotes better muscle tone.
But as your vet said, it's not even yet known IF this is a urate stone? It might also be a slug egg that was retained- you'll find out soon enough. Snakes are living creatures like the rest of us- and some things just "happen". I sure HOPE the pink tinge on her underside isn't sepsis- no way to know "from here" either. All the best- please do let us know the outcome (no pun intended).