It's very inconvenient to always have to "debug" the application to run it. I tried to research this, but it seems there aren't any easy-to-find articles on this.
Do you think that the problem is only with the CubeIDE not being able to detect none-originial MCUs/linkers but that it works with others? Do you also use the mini st-link v2 USB?
I have this exact problem, though when using CubeProgrammer, it does upload to the Blue pill. However using the CubeIDE, I get this error message trying to flash it. Are you sure the actual chip was the problem?