Just to add some more random suggestions, I'd really stress that reference
@ironass made on doing Factory Reset. And don't forget to remove your Google account too.
Given the amount of available system resources available on a S2 and that this apparently will be more of a single-purpose phone (media player), you'll want to make as much of those resources free for whichever media player app you've opted to use as its default so uninstall or disable as many apps as you can (be judicious but also don't go crazy and disable so many things that it limits basic functionality). Samsung included a 'Standard mode' and an 'Easy mode' buried in the Settings menu, you might find selecting Easy to be more suitable for this kind of situation.
But getting back to your original query, that playlist issue could be due to a number of different things. Depending on the application you used on your PC to create the playlists, it simply might not correspond with using them elsewhere. Some applications are more universally compatible, some more proprietary. Also, just which app are you using as your default media player? The Samsung default app? Google Play Music?. Third-party apps tend to have more functionality and more extensive feature sets so if it is a matter of metadata, do keep in mind that Windows or Mac (not knowing just what kind of computer you're using) handle such things differently than Android so there are always miscellaneous incompatibility issues. And instead of editing metadata on individual files (an issue if you eventually end up with a media library with hundreds or more of audio files), you might find it more prudent to just install a playlist creating app on that S2 and just make new, compatible playlists. If you don't want to go that route, there's also the question on which media player app you're using. There is no set rule that every app has to be equally capable at everything another app is, most have a lot of variance on functionality and appearance. You might find Stellio Player does work out better at finding your music files and handles your current playlists as is. I'll also suggest trying out the VLC app, it's free, no ads, and handles a really wide range of file types/codecs. And on a side note, since this is obviously just a retired phone you're bringing back to, if it is no longer tied to a Google account and access to the Play Store is problematic, you can use a source like apkmirror to manually sideload the necessary apps:
Stellio
https://www.apkmirror.com/?post_type=app_release&searchtype=apk&s=stellio
VLC
https://www.apkmirror.com/?post_type=app_release&searchtype=apk&s=vlc
Note that the latest versions 'might' not work on whichever version of Android that S2 is running so you might need to experiment to find the latest old version that does work. (Typically installing only from the Play Store is recommended, and the Play Store will determine just which app versions get installed on each respective Android install.)
As for managing your music library, it sounds like you're doing a lot of it through your computer. That's more of a convenience issue than a practical one since if you are using Mac or Windows, that also rely on entirely different file systems, there are limitations on what you can do on any device that's running a different operating system (in this case, Android). Samsung does include a basic file manager app, My Files, which is a more direct way to manage files and folders on your phone (just look in your Apps folder for 'My Files'). But My Files does, by design, have some integral limits on features and capabilities, with a plus being there are plenty of very feature-rich, third-party options.
