History of this one surprised me. The Millerhill avoiding line was not (as I had assumed) electrified with ECML but instead only much later by "Edinburgh Crossrail" in 2002 but only from Newcraighall to Portobello Jnc, not sure what electric service used that but I think it would have been overridden by Borders Railway. Electrification was extended from Newcraighall back round to Monktonhall Jnc as part of the EGIP project in 2017 for the Millerhill depot
I'm going to have to check your facts on this one I'm afraid.
The line was electrified back in 1991, and somewhere I have pictures to back that up. The line was first regularly used to shuttle electric locos backwards and forwards from Millerhill, and electric freight via Waverley, to and from Carstairs.
The first regular passenger associated workings were the 90s and mk. 3 sets while they were working the North Berwick turns. The locos, sets, and the 90s working the sleepers, were stabled at Millerhill between turns.
Although the line was electrified for the entire direction of operations to Newcraighall, no electric unit ever ran the shuttle, mainly because they were usually extended through to Dunblane, Bathgate, or latterly Fife, interworking with pure DMU routes on the other side of Waverley.
Furthermore, ScotRail didn't have enough EMUs over at Waverley, with the North Berwick line worked by the shortened rockets mentioned above, or with EMUs from Shields, cycling through on "via Carstairs" turns.
That led the line to be a bit of an oddity, with the decline in ECML electrified freight and the reversion to EMU operations meaning that the wires through Millerhill were basically unused for about a decade.
The building of the Millerhill EMU stabling sidings led to the wires being used very regularly indeed, however the Monktonhall to Millerhill sections remains poorly used.
However one particular oddity of EGIP was the provision of a fully signalled route through the yard, up to passenger standards, which may be where the confusion is coming from. In the end, the fully signalled route is in limbo, and is only needed fully in association with a future Waverley to Craigentinny blockade, but work has been done and it is still there, sitting not yet commissioned on top of the existing signalling.