I have a few dozen videos there, and about half of them have the comment that the video contains copyrighted content. And this comment appears there a few minutes after uploading, monetization is removed from such videos. Where can I find non-copyrighted music?

For example, a long time ago I had a video with the music of Ramstein on YouTube, at first there was just a notice, then the video started to go without sound in Germany, and then the copyright holder drastically changed its policy, and the sound was turned off altogether. Now if you find that song in the YouTube catalog, it will say that you can't use it in your videos. So you have to use non-copyrighted music.

And where is the easiest place to find copyright-free music like this? Can you advise me a good service or composers who create inexpensive music and from them you could buy music without copyrights.

You should use services that provide music without royalties, such sites are very easy to find music in different categories and at low prices. Here is one of the services where I find copyright free music, here you can find everything you are interested in. All music in my videos on youtube was taken from this site. Subscription price is not very expensive. You can choose the quality of the music by yourself and download it in certain short segments.