That's fine but that isn't what I wanted to emphasize.
My point is that if you're at a Big Corporation, both you and your manager are embedded in a bureaucracy. Your manager can't single-handedly wave a wand and get you a raise on his own. He/she has to convince his superiors and Human Resources to get you a raise.
You need to imagine what your manager's bullet points would be to argue on your behalf to convince the company to increase your salary. What are your leverage points?
E.g. your role in data science work is crucial to release a $200 million product on time in the next 6 months. If you leave, everything falls apart.
On the other hand, if you have no leverage and want a raise outside of the annual review cycle and while doing the same work with no promotion... that's a harder sell for your manager.
To put another lens on this, if your manager goes to his boss and HR and says I can't lose Ralph, he's indispensable... Likely his boss and management will criticize him for building an org which has indispensable people in it.
> I have a good relationship with my manager, but I feel it hard to break the ice with Salary topics. It really hit my nerves
At various times I've had a lot of anxiety regarding my job, especially when I was feeling financially vulnerable.
Regardless of how you handle this particular situation, you might try to work on the anxiety issue. You might consider a few trial session with a professional counselor. The human psyche can be pretty non-intuitive, and a good counselor can teach you a lot about how yours works. It like discovering a (partial) owners manual for your own brain, if you find the right counselor.
That could be because they don't want to discuss this topic. It's like trying to hit on a person who doesn't want to be hit on - pretty hard, likely a 'no'.