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I'm on 2023.44.30.9 and I haven't seen a big difference between 2023.38, apart from when it nags it will display a warning message, whereas before I'd get the blue sky and sometimes a beep. I haven't had a yellow card, yet.
By the way, my car insurance (Churchill) states that the car should always be running the latest software.
Unless your Churchill policy is worded differently to mine that clause doesn't apply (yet). If it was a self-driving car approved by the Secretary of State for Transport then you would need to keep the software up to date, but as it's not then the section does not apply.
Problem with not updating is, inevitably there will be a security update that will be mandatory as part of a recall, and at that time i bet Tesla will force the update onto the car, because they have to.