I have taken this alternative from this list of software, also privacy oriented. It is an open source frontend of Youtube Music, which takes inspiration from Invidious.
You can install it as a PWA, which is quite valuable for me, because (as far as I understand) PWAs use the privacy level you have configured in the browser where you install them.
The only downside I see is that it uses Cloudflare, under US legislation. To my taste, I would prefer it to work under Swiss law, but nothing is perfect in this life, I guess.
Even so, I've been testing it on my mobile as Brave PWA and my experience is quite satisfactory. It serves as a perfect replacement for YT Music, Spotify, Tidal, AMZ Music (unless you like podcasts, which it doesn't cover, to my personal misfortune).