Writing music is a strange genre to curate — you need something interesting enough to stay on, but not so demanding that it pulls your attention from the page. Dark country and atmospheric americana sit in a useful spot for this: the lyrics are usually coherent, the production is uncluttered, and the tempos are slow enough to read against.
Sixty tracks below that work as background without being boring. Free downloads, lyrics on every page (occasionally useful for fiction-writing prompts), no signup.
Easier setup: leave the 24/7 radio stream on in another tab. Same catalog, on shuffle.