Congratulations on the MBB offer! Regarding your question:
Q: Assuming I'd want to switch to McK in the future, will I need to take the PSG again or will my previous score be valid?
The score is valid for one year. So if you apply after that and they are not considering you as an experienced hire, yes, you will likely have to take it again.
If you apply as an experienced hire, it depends on the office and the experience you have. In some cases you don’t have to do it, but I recently helped a candidate with 9 years of experience and they asked him to take it.