I've never seen a Vyse Street on any map of that area. The roadway you show in the picture is the entrance to St Mary's Church and the Priory and I don't think it ever led anywhere else. However, it may well have been called Vyse Street.
The area south of this roadway (approximately where you've made the red marking) used to be the quite extensive church graveyard. This was cleared to make way for Cammell Laird
's new dry dock, which opened in April 1962.
There used to be a Mersey Street just near here, running down to the riverfront by the old Birkenhead ferry.