Tests usually cannot prove absence of defects. But they can show presence of defects. So yes, a test suite that runs without errors tells you “nothing” in a way

Tests usually cannot prove absence of defects. But they can show presence of defects. So yes, a test suite that runs without errors tells you “nothing” in a way. But it's a very good safeguard to ensure that code changes don't inadvertently introduce unexpected changes. For me it's also the case that I think much more thorough about what inputs could be possible and potentially problematic, so there's often an extra set of test cases around boundaries of input values that would have never been tried when just quickly throwing together a demo application to showcase and experiment with a new feature. But the fundamental problem that lots of bugs don't appear in testing since those code paths are never tested also means that testing alone isn't sufficient. But I guess we all know that by now, and combining different kinds of tests with other approaches like code reviews (actual proofs are probably beyond the scope for the vast majority of software projects) is being done all the time to not bet everything on a misguided 100 % code coverage unit test approach that's both expensive and fairly useless.