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.
The “established” meaning has in fact been deliberately created by megacarporations like Microsoft so they can exploit free labor by volunteers to make money without lifting a finger. Look at who is sponsoring the OSI.
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.