I am an italian citizen, but my residence is in the United Kingdom since 2016. I currently hold an EHIC card from Italy (which might not be "valid" anymore), and an EHIC card from the NHS (my current healthcare provider).
In the event of a no-deal Brexit, UK citizens wouldn't have access to free healthcare in EU countries as they currently do, and they would need to travel with a health insurance (just as any other non-EU citizen).
I was wondering: would that apply for me as well? While an italian citizen (so an EU citizen), I would be a resident of a non-EU country. I would be covered in Italy because of how the italian system specifically deals with italians living abroad that temporarily visit. But if (hypothetically) I travel to France and I need urgent care in a hospital, would I get it for free? And how exactly?