But that what East Coast buses is, FSE/Bluebird are two sperate licenses.
To be honest, I think you're confusing yourself between TUPE, legislation, operating licenses etc
TUPE is a statutory piece of EU legislation (though it can be interpreted slightly differently in different countries) - it basically protects your established terms and conditions (but not pensions) if the business that you work for is purchased or the activities that you are engaged in are transferred to another business. There are many firms that have a multitude of different terms and conditions for employees because of TUPE. How this is then managed is not proscribed. Some may set up separate firms but the vast, vast majority don't. They employ a range of different internal measures to manage this variance or they ignore it.
So what of separating firms and operations. You can have a separate O license but you can, of course, have any number of liveries and brands on a single license. TC's have also sought for operators to reduce the number of O licenses they have (e.g. the amalgamation of the two First licenses based on Bristol).
So if not a new entity, why a new brand? They probably have their own reasons such as fare structures?
What is is different from the Musselburgh and North Berwick ones is (as described already) where the operations and business had to be placed in a state of torpor at the instruction of the CMA whilst they assessed whether to allow or demand divestment.