From what I've read they invested $80bn in 10 year mortgage-backed securities to generate yield when rates were down at 1.5%. So it sounds like a huge asset-liability duration mismatch. Which bit them when rates rose and people started to withdraw for better yields elsewhere - yields which SVB couldn't afford to match.

According to this article they were already $15bn in the hole (on their HTM portfolio) at last year-end!
https://blog.argonautcapital.co.uk/articles/2023/03/10/silicon-rupture/

It's shocking to me (as a non-expert is US banking) that they were allowed to continue to operate in this position. How do they pass any kind of stress test with this balance sheet? And why weren't they managing their duration mismatch / hedging their interest rate risk to begin with?

Films like margin call give the impression that US banking is all hyper-technical rocket-science. But these guys appear to have failed because they couldn't manage interest rate risk. It beggars belief.