Our Federal tax payment has been debited and our state refund has arrived but our status is still 'Accepted', not 'Approved'?

Your status in your TT account does not change after it has been "accepted"  --   TurboTax will always just show that the return you prepared using the software was accepted.  TT never knows when, if or how you paid your tax due, or if you received your refund.  No updates are sent to TurboTax by the IRS or your state.

The "Accepted" only shows in your TurboTax account. Nothing more gets sent back to the software provider after the initial acceptance.

The "Approved" or "Processing" only shows on the actual IRS's Where's My Refund page.  A state's own WMR page might have it's own terminology.

https://www.irs.gov/refunds/what-to-expect-for-refunds-this-year