The approach they seem to be following is to initially wire only the minimum amount to allow battery trains to take over a route (subject presumably to some prior design assumptions concerning off-wires capability). Thus on the Borders line they are only wiring from Tweedbank to the south end of Bowshank tunnel, and from Newcraighall to an arbitrary point north of the City Bypass bridge. Then presumably they move on to do somewhere else.
I'm hoping for at least two events in 2023 that should clarify the proposed sequence of events:
1) the first review of the overall decarbonisation strategy, which in the original document was scheduled for spring 2023.
2) further details on the procurement of "suburban" EMUs and BEMUs.
In possible partial answer to
@numtot12345 's question, it was recently reported in the Haymarket-Dalmeny thread that the Forth Bridge is expected to be fully electrified by 2030. It's a reasonable guess that that means continuous electrification of at least Edinburgh-Dundee via Kirkcaldy and the Tay Bridge by that date.