The B4562 does exist on OS maps. It's marked as a secondary road leading from A469 to Newport road (B4487) following Lisvane Road, St Mellons Road, Bridge Road and Tyr Winch Road.

Since OS still recognises it as a secondary road I would suggest upgrading the entire length of the B4562 to a secondary road matching that of OS Maps and falling into line with other major maps.

If I have time tomorrow I might go ride that way and see what state its in with all the new builds.