This is a great example of a 'Twisted Turnout" I have found many examples of this handrail detail

and they all seems to be used with twisted newel posts and balusters. The stair brackets are raised panels with a detailed scroll behind it I feel this is a old England stair detail.

The "Twisted Turnout" creates a very graceful elegant entry on to the staircase,
The baluster profile and alternating pattern makes this look very detailed.

This is a very unique handrail profile, its very wide with 3 step down edges,

 the profile running through the rail caps is a very nice look.