Well-heeled demi-mondaine provides American capital (8)

I believe the answer is:

richmond

I'm a little stuck... Click here to teach me more about this clue!

'american capital' is the definition.
(state capital of Virginia)

'well-heeled demi-mondaine' is the wordplay.
I cannot quite see how this works, but
'well-heeled' could be 'rich' (similar in meaning) and 'rich' is located in the answer.
This explanation may well be incorrect...

'provides' acts as a link.

Can you help me to learn more?

(Other definitions for richmond that I've seen before include "Sweet lass of - Hill" , "Yorkshire town close to Catterick garrison" , "Thames-side town" , "Capital of Virginia, USA" , "Just copes" .)

I've seen this clue in The Independent.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.