How does one would probe for it? I have tried researching using
Glassdoor, but it gives either huge variation or no data for the
companies I am looking for in it. I have asked HR persons directly,
but most of the time they say "it all depends on the experience / what
you show on the interview".
If a company posts an open position, and it doesn't contain a salary range, you often cannot estimate what they will actually pay. Some companies generally pay well, some do not - and that is reflected in Glassdoor. And as your HR contacts have indicated, "it all depends" is almost always the case.
You should consider working with an agent.
At least in my part of the world, there are many companies who will work with you to find a job. The good ones have lots of contacts in many companies, and will know the salary range of positions that are being filled.
According to my stats 3 out of 4 companies I was interviewed with say
"Yes, we would really love to hire you, but that's too expensive /
budget does not allow it" when asked to match my current salary.
That might mean that you have priced yourself out of the market for your position. Companies don't pay unlimited amounts for particular positions. You might need to consider your career ladder and seek positions that are higher on it.
Interviewing for different positions is not really possible: it's
already a top of technical ladder, and I have no intention to switch
If you are truly at the top of your particular technical ladder, yet wish to stay in your technical position, then you might need to consider other variables.
Perhaps you might need to seek very large companies. Sometimes their ladder goes higher.
Or you might consider changing locales. Top pay varies by country/region.
Or you may just be maxed out, and might have to settle for smaller raises over time.