Hi,
You're likely not doing anything wrong, iTunes may be failing to operate quite as it claims. The operation that is supposed to let you change your media folder doesn't stick. Instead of trying change via preferences you need to move (as in cut and then paste) the location of the iTunes folder with your library in it to say D:\iTunes. Hold down shift when launching iTunes and use the choose library option, then open D:\iTunes\iTunes Library.itl. The media folder location will likely have reset to D:\iTunes\Tunes Media, but it is best to check before proceeding further. You should now use File > Library > Organize Library > Consolidate Files to copy in any content that you've managed to add to the library from alternate paths when there might not have been enough room to copy to your system drive library, or that you had otherwise manage to get linked at its original path, rather then being copied into the media folder.
The drive letter D: in the example is arbitrary, any letter is fine. A larger internal drive might be best, with an external used for backups.
When you delete content from the iTunes library you should only get a prompt about deleting the files if they are inside the currently selected media folder. Anything linked to the library that is outside the media folder never gets deleted, and thus never generates a prompt. Test that concept with something you've already made a backup of. Personally I would manually move such content to an alternate path first, e.g. D:\iTunes\Removed\ which would mean that iTunes could no longer find the files, then select and delete the entries in the library.
If you also have iOS devices that you want to be able to backup to your computer, but it has a relatively small system drive see Relocate iOS device backups. A change in forum software makes some of the text hidden, and the lettered steps I wrote were changed to numbers. I really need to take the effort to update it properly, but the page also has a longer and probably jargony version of the first paragraph above I wrote when I was trying to make something that would work for those with still limited space for manipulating things or didn't want the default iTunes naming rules.
See Backup your iTunes for Windows library with SyncToy - Apple Community for advice on backing up.
tt2
