Rail Alphabet 2 + the “return” of the BR double arrows + black-on-white signs + GBR are all being spearheaded by the same people so they are very much interlinked.
I'm not sure it's true that they're interlinked in this way.
Rail Alphabet 2 appears to follow a similar vein to when TfL had their Johnston typeface modernised and remade into Johnston 100, I don't think it's a coincidence that Peter Hendy has been the chair of these organisation when both of these things happened. He was very involved in the Johnston 100 project so it makes sense he would have also wanted to see the return of a modern Rail Alphabet to replace Network Rails ageing signs.
GBR appears to have sprung out of various factors, namely the Williams review initiated the general idea, then the review was kept pretty quiet for a bit and then it was then kicked into gear at the start of Covid when the privatised system collapsed in on itself.
I don't believe that the signage and GBR both happened linked together, I think it was just a case that they happened to take place at the same time separately and ended up stuck together when various outside forces changed things.