Why can't I search iTunes for a specific song or artist anymore?

Are you showing the "iTunes Store" in the left side panel? I believe it is hidden by default.

You can toggle it on and off while in the Music app by going to the MUSIC menu > PREFERENCES > GENERAL and toggling on the iTunes Store option.

On iOS, you need to use the iTunes Store app, which is separate from the Music app.

If you are referring to the Music app on your Mac, that feature is still there, but it is buried a little bit.

Click on SONGS from the left side pane to display a list of all your songs. Then press COMMAND+OPTION+F to bring up a filter box. I use this all the time to find artists and songs.

This also works if you select ALBUMS or ARTISTS (or really anything) from the left side pane.