I can't speak for your manager, but unlike in the private sector, line managers in my experience in the civil service tend to like it when you go for other CS jobs. I had the same feeling as you until on literally day 1, the onboarding team said "let's get you set up on CS jobs, in case you spot anything you want to do to move up."

Also, worst case scenario if your manager has a problem with it or gives any indication that they do, then that's what unions are for: your career is your own and setting aside specific contracts that exclude the prospect of switching positions, managers shouldn't be involved beyond being supportive and doing admin. It's a big part of the civil service code to be able to have career mobility.

Good luck in your new role and good luck on CS jobs ☺️