When you open the window to add your demo, you need to click on the "Web" tab in the upper right corner. Then copy and paste the link to your song in the space provided. Hope that helps!

If its marked private at Soundcloud even if using the web tab sometimes it doesn't seem to embed, but that could also just be issues on my end, wouldn't be unheard of

I have not used SC in a while due to all the issues... and spam, and etc., but I remember, as mentioned by @dzd just said, that if not "Public" did not embed and then in the Liner Notes, I/We put the literal URL Link there and some how flagged for folks to see [***] or etc.

Or, one could consider a BandCamp just for this since those wav files (wav only there), link. However, no player embed if that's the "point" (?).

It seems, maybe about 2 years ago... folks had less of a problem, clicking the direct link from the 5090/Fawm frame since we all know those domains.

Get funky with "other" hosts and many are more careful then.

I, also, have one of most kinds of popular browsers used to view stuff with, -- and they all tend to engage differently with no predictable "gotcha", -- why. A wide open Chrome Book which is that browser as OS seems to run anything and if not on "that"... well, just the normal Net weirdness then.