Austerity is a policy choice, it has nothing to do with the cost of borrowing. States that control their own currency, like the US, the UK, Japan etc. do not borrow money at all. The term is simply not applicable.

During the COVID crisis deficits grew rapidly and the cost of borrowing did not change. This only happened after the crisis was over, and as a policy choice, not necessity. Japan never increased interest rates and its deficit has continued to widen.

The credit markets do not sustain the UK. It is the other way around. Without the UK state there would be no credit markets, at least not in GBP.

I think the core problem is that it is your thinking that does not map to any observed reality.