Your media player.

Hmm... Maybe I misunderstood you, but iTunes and iPod work perfectly with the familiar MP3 format, and there's no need to convert anything. All tracks added to the library are copied (or moved, depending on the settings) to a separate folder, from which it is also not difficult to extract them.

The iPod overwrites them. I don't remember if the format changes, but otherwise, it saves to a hidden "Ipod Controls" folder, and all the music is stored in a bunch of small subfolders, and each song has an abbreviated name.
That is, if usually (probably:)) you store music, for example, in a folder called "Music", then in a folder with the artist's name, then a folder with the album's name, etc., then on the iPod all the music is stored in a completely different order, and it is not very convenient to transfer it back to the system manually, at least because of renaming (you need to check if the format changes, maybe it doesn't).

I switched to iTunes after Winamp killed my library for the second time, in the sense that the files remained on the disk, but disappeared from the Winamp library.

With iTunes, there will be the opposite problem:) if the files are deleted on the disk, then it will not be so easy to get them out of iTunes (at least from the iPod:)).

I didn't understand this at all. To transfer the library intact to another Windows or another computer, you have to make a backup copy of it on rewritable disks (this is especially necessary if you want to save the playback counter, ratings, added lyrics, and other unique settings that are not written in ID3 tags).

Well, again, you are transferring all this in the "iTunes system", and not in the basic (Windows?) system.

That is, iTunes, roughly speaking, has its own library, and you can only access a separate file in it through it.

I hope I expressed myself more clearly now:)
To be honest, I never dared to delve into all the intricacies of the program, so I use clumsy language when partially explaining how it works:o