Thank you for the responses, much appreciated. Coolant check was performed when completely cold.
There's no service history, but I had budgeted for the cooling system overhaul
3pedals your breakdown is great, cheers. Based on that, it seems likely to me that:
it has a faulty sensor and coolant has been overfilled in response.
or
it has a leaky HG.
I highly doubt any recent maintenance, and can therefore pretty confidently rule out improper bleeding.
Now I just need to decide on a PPI or walk away. Still confused about why the warning would occur only after turning the car off and not during driving, but I have a better understanding of the situation now. Thanks all