I believe a songwriter needs a journal—a primary container for your songwriting work. Expect to fill a series of these over time. In your journal can go not only actual song drafts but also pre-writing or supporting material: object writing exercises, back story writing, rhyme worksheets, project ideas and the like. Get accustomed to the idea that you can write stuff down that may not look anything like song lyrics, to help you get to the final song. Some materials, like rhyme worksheets, could be resources used for multiple songs.
Every songwriter needs to sort out their own approach to keeping their songwriting journal, and specifically boundaries or separations between that journal and other material you want to keep in journal form. I’ve spent many years honing my own “life and art journal architecture” and the design is constantly shifting. Here’s a picture of the archive of most of my 160+ journals, dating from the Tarot card “research diary” I started around age twelve: