There is not much I can add to Wheat's excellent answer.
As Wheat said, newer material is not likely to have sheet music included in the document submitted with the copyright registration package. I am a songwriter and have registered my copyright on many of my songs. But these days all I have to submit is a copy of the lyrics and a recorded sound file (such as an MP3) for the music. Before being able to upload MP3 files through the internet, songwriter's and composers could register a copyright on a recorded work by submitting a cassette tape or CD via the mail.
I am guessing that prior to the ability to register a copyright on a recorded work, that it was more common to submit sheet music or something akin to it. Songs and musical compositions registered with the US Copyright Office are available to the public for a fee. To learn more about how to search what is on file at the US Copyright Office and obtain copies thereof - click this link Obtain Copies from Copyright Office
Obtaining a copy of a song from the copyright office, does not give you authorization or license or the right to use the copyrighted work for commercial purposes - or to reproduce or copy it for distribution to others. But if you use it to learn to play a song at home for your own enjoyment, I think you are safe.
You can purchase sheet music with full music notation for multiple instruments (including piano) from numerous sources. But most of those are arrangements written out by someone who interpreted the original artists or songwriter's work. Many of these arrangements may have been created under license or with permission from the copyright owner, but that still does not mean it was the original songwriter or composer who wrote the score or notation.
In probably more cases than not, the original writer or composer my have never written any sheet music or score for the song (I never do - and neither do any of the song writers I know) - so the only thing that will ever be available is sheet music created by someone who interpreted the song and arranged it according to what they hear in a recording.
If the song you want to play is a popular song, it is very likely that someone has taken the time to create a very authentic arrangement and published it (perhaps with permission) in fully notated sheet music form. If you have not already tried it, I would enter Song Title Sheet Music in your internet search engine and see if that yields some results. Alternatively - search for sheet music by the artists name as opposed to song title. Often entire song books of sheet music are published for songs by a particular artists or for all the songs on a particular album.