This has been discussed many times here at least in reference to copyrights. The general consensus is that once you document your song's © date via uploading it to SC, YT, etc., you are good w/o going to the trouble of actually copyrighting it formally. The upload date stamps it for time immemorial.
We have 22 songs licensed via Songtradr to a very large worldwide company and we've never copyrighted a one. We also have many songs on Apple Music, YouTube, Amazon, Spotify, etc., that have been "formally" copyrighted.
And, honestly, unless you have a huge hit what are you gonna do if somebody steals it? Take some of the few cents it earns streaming, etc., and sue?

FWIW I'd throw it up there and not worry.
Bud