The most common definition of "open source" is pretty much indistinguishable from free software. The only real difference is the overall goal of the two movements. The term open source comes from the OSI: https://opensource.org/ The definition of "open source" is here: https://opensource.org/osd Before the OSI nobody used the term "open source". It was coined by Eric Raymond (ESR). I can't think of any way it would be correct to use the term in a different context.

>Open source does not have to be free.

If we're using the common definition that everyone in the industry uses, then it actually does.

In fact, Open source was coined in 1998 because we needed a term with a precise and well defined meaning.

I don't know anyone who uses the term open source in the way you describe.

So, it's source-available, not Open Source.