I think something else is going on at this company, based on my experience of both sides of this one (recruiting manager and applicant)
TLDR - don’t waste your time with feedback, it’s politics and not your fight. Only communicate if you are asking a genuine question.
Longer: in an “important international group” it may be wrong to think that there is a common viewpoint within the company of hiring and salaries. Such companies are often very fragmented and consist of empires within empires. My experience was of a very large European aerospace company (the obvious one).
The hiring manager may have a picture of what they would like to achieve within the company, but they may not have any real buy-in from their own management of the job-levels (and salary) of what it would take to achieve that. So, they may be fairly untruthful with their own management in getting the “allocated headcount” and even more so with the applicants, telling them whatever they want to hear.
In my case as an applicant, I was recruited at 25% below market rate to “head up and start a new department”. I accepted because the technical area was so interesting. The actual job when I turned up wasn’t what I was sold by the hiring manager. It matched the salary, not the job description. There was no strategy at all in place, the starting team of “two or three” turned out to be a single summer student plus somebody seconded to another project in another country, it was just a desk with a phone and laptop. It later turned out that my boss literally didn’t even have a budget for that desk and phone - I had to find ways to sort that out for him from other project managers budgets.
The wonderful job title was pure grade inflation.
“Human Resources” in a company like that is just doing the paperwork. They have no connection to the decision or outcome of hiring; any feedback you give just sits in a contractors inbox. There isn’t any mechanism for feedback to get to a decision maker.
Oddly enough, because I am the most stubborn person imaginable, I stayed for five years, and built up a new department of ten people from nothing, through sheer graft and hustle, with zero support from my boss.
Along the way, I did what I had to do, and I’m ashamed to say I told similar half-truths to internal project managers and external applicants as I built up the business. Because it was the only way to make stuff happen. The company culture was deeply toxic. Fortunately, the department I built was successful in my hustle, and those half-truth chickens never came home to damage anyone.
It was hell, and honestly I mostly just did it because I couldn’t admit to my wife and friends that I had made a mistake taking the job. Was it rewarding? I’m kind of glad I did it, just to prove that I could.
Would I do it again? Hell no.
Notice how nothing I’ve said is anything to do with salary. On the one hand, the satisfactions or pains of a job often matter much more than the salary. On the other hand, the salary is the one thing they can’t fudge* as to whether the role matches up to what they are telling you.
Back to “what can/should you do”?
If you’ve decided that you are no longer negotiating for this role (because this will kill it, but might set you up for something else), you can say something like this: “I’m looking for a salary at least £X, based on the skills I demonstrate in my current role and the value that I can bring in future roles. I think I’m ready for a step up in responsibility [Cough Big Companies Love Flattery, Cough], are you looking to fill any more senior roles?”
Reason why I suggest this - they might be about to advertise an adjacent role in what you would normally not consider a match, or even “too managementy” if that’s your inclination. But, they’ve basically told you that the job description they advertised isn’t what they are prepared to pay for anyway.....so you might find that “the next step up or two” (in their minds not yours) corresponds to the type of job you want and think you applied for. And that one will also be unfilled for exactly the same salary reason.
And secondly, this will not be responded to by the hiring manager for the first role, but by a contractor HR person who has no skin in the game. As far as they care, if the recruiter wants to know which vacancies are open, they will tell them and send the job spec. Which might well be unfilled for the same salary reason, because the job description is.....optimistic....and the right people aren’t applying.
Then, maybe you get an interview for the other role and see.
