I have read How to Win friends and Influence People and I haven't felt like its manipulation.

[I can be wrong and I usually am ;)] but the book teaches just some way to better re-phrase your best intentions and I have started to think the phrases in my head...

Just be honest with people is what that book taught me. I highly recommend people reading it.

Now I will be honest that reading the book itself isn't gonna give you something. It depends highly on variety of factors. For example, the book also teaches to listen more often and I genuinely try to do it as well but I sometimes fail to do that as I am a bit expressive/talkative

I think it also depends on who you are and how the book reinforces some particular topics. You dont have to completely do everything the book says to have meaningful impact as then it would feel manipulative to other person, yea.

And at the very least, reading this books makes you aware of some logic behind what he's saying (for example. I speak a lot but I should listen more, because people like me are so many and everyone likes to speak and be heard but people who actually listen are rare)

and then I can realize that I am speaking too much and so I think that I am more aware.

More Awareness of a topic doesn't mean complete and utter mastery of it but long term persistence of that awareness helps out meaningfully.

TLDR: Just be yourself and see if something sticks from the books and to implement it slowly and the way you like. There isn't one perfect way (not one even in the books) to living life. At best, its collection of what other successful people are doing. I wouldn't suggest (completely) living off the books because you have your own life and way of living it and you should be honest about it to yourself as well.