Tests can't catch race conditions in multithreaded code. Now that I told you what the tests can't catch, can you imagine writing tests for that specific thing?
I've written tests around multithreaded code, but they typically catch them in a statistical manner - either running a bit of code many times over to try and catch an edge condition, or by overloading the system to persuade rarer orderings to occur.
tsan will catch a bunch of potential race conditions for you, under the condition that you run it somehow. How to make sure it's run? Well, add a test for the relevant code and add it to your tsan run in your CI and you'll certainly catch a bunch of race conditions over time.
This has saved me a bunch of times when I've be doing work in code with proneness to those kind of issues. Sometimes it will just lead to a flaky test, but the investigation of the flake will usually find the root cause in the end.
I’ve written tests to do exactly that, by adding carefully placed locks that allow the test to control the pace at which each thread advances. It’s not fun but you can do it.
There's also https://clang.llvm.org/docs/ThreadSafetyAnalysis.html which can statically catch some threading issues, though I've not used it much myself.