Looks like the popular depression and anxiety tests are pretty valid but also non-overlap between test items indicates that they're overly broad terms.

The fact that you don't understand overlap as a layperson doesn't indicate that a test doesn't test for a real thing. On the other hand the DSM-V categories are likely not the best possible label. That even the NIH opinion who declared that they are willing to fund studies that don't use them and try to find new categories.

If you want to dig deeper in how to think about such terms "How to think straight about Psychology" by CFAR advisor and professor of psychology Keith Stanovich is a good read.