The general test suite is not proprietary, and is a standard part of the code. You can run make test. It uses TCL to run the testing, and covers virtually everything.
There is a separate TH3 test suite which is proprietary. It generates C code of the tests so you can run the testing in embedded and similar environments, as well as coverage of more obscure test cases.
This isn't an issue as SQLite doesn't accept contributions because they don't want to risk someone submitting proprietary code and lying about its origin.
I've never understood why other large open-source projects are just willing to accept contributions from anyone. What's the plan when someone copy-pastes code from some proprietary codebase and the rights holders finds it?
If the rights holder is particularly litigious then I could see them suing even if you agreed to take out their code under the argument that you've distributed it and profited from it. I don't know if there's been any cases of this historically but I'd be surprised if there hasn't been.
There is a separate TH3 test suite which is proprietary. It generates C code of the tests so you can run the testing in embedded and similar environments, as well as coverage of more obscure test cases.
https://sqlite.org/th3.html