When they ask for your salary, you can be vague and say “My current salary is around the lower end of that bracket so I’m looking for something in the middle to upper end of that”
Also, they’re looking for the person who can do the job the best, not who is cheapest. They have had that bracket approved so if they need to go to the top end, they can and will. It’s just about proving you’re worth the top end of that salary rather than them wanting to save money. That’ll be done by someone else and not the interviewer.