Yes, I agree that "source available" is an accurate description. Unlike "Open Source" licenses, which have no restrictions, "O'saasy" does not allow you to do "anything" you want. Adding a clause like "but you can't compete with us" makes it incompatible with OSS licenses.
I am fine with licensing your code as you wish, but I will always oppose attempts to redefine the widely understood and established meaning of "open source" that has been in place for over 30 years. You don't get to change its definition.