You are correct.
It gets a little worse with YouTube Music. Uploaded tracks can't be downloaded as mp3, unlike how Play Music did. As with their streaming music, these are only for use in the YTM app. To get your files back, you have to use takeout.
This has been a longstanding issue with cast support so far as I can tell. It's been mostly working for me lately, but I couldn't venture a guess as to why.
I hope this does get added. In my extremely limited testing, Poweramp EQ seems to be more consistent than wavelet, and wavelet seems to have a newish bug that causes it not to say what apps are using it.