The cross border TOCs here are a bit of a red herring.
Obviously, nothing is going to change with regards to LNER and Avanti operating to Edinburgh and Glasgow. TPE and XC will continue to run to both, although there are likely to be some changes made there.
The majority of journeys made on the cross border TOCs in Scotland are cross border journeys. They will continue to be subject to pricing and through ticketing set by the DfT, perhaps with some ScotGov input.
The difficulty with intra-Scottish journeys is primarily going to be pathing and allocation of ticket revenue. XC are reasonably likely to cease running to Aberdeen, Dundee and Glasgow in the medium term, with services curtailed at Edinburgh. With LNER these services serve a useful function, and they will continue to exist.
Revenue will be shared depending on how LNER goes with advance only tickets. The only other ticketing issues are Reston, Dunbar, Motherwell and Lockerbie stations, for which what is currently in place will continue.
Apart from that:
Infrastructure will have to be devolved at some point to allow more integration and control from ScotGov. I don't expect standards to change north of the border.
Timetabling will still be joined up between the regions, although I'd expect a rejig of the north of Edinburgh services to fit any increase in Scotrail domestic services.