Carry on applying to give you options.
What are the starting salaries for similar mid-career, experienced roles.
If you are not desperate and you have some negotiating position if you are contracting. Covid has caused problems but to some extent, you risk rebasing your career history and salary history to future employers adversely.
I would put the ball in their court again. The rationale about fairness to other recruits will not pay the bills and is just a hook to negotiate, unfortunately.
Even in the public sector where the notion of fairness is embedded, there is often scope to offer higher starting salary within a range where appropriate.
Repeat your point about your salary of 14 years ago when you have a broad skillset and experience. And tie them into a firm commitment to a further payrise after a 3 month probation rather than a vague promise. That shouldn't be impossible from fairness.
This is your main opportunity to negotiate and to impress them with your brokering skills. Once you are there, they probably won't magically become a kind and generous employer and, even if they do, that won't pay the bills for the next few years. I suspect this notion of fairness across the team will be selectively applied.
Good luck.