You are correct. Current tests are only for covid. They can be designed to test for both, and many companies are developing such tests now so that, during flu season, they know what you have.
The notice you are referring to in your reply to me says that, starting Jan 1, 2022, labs must use a test that has gone through the normal pre-market approval process, which none so far have gone through because they were launched under the EUA. They encourage that tests be designed in the future to distinguish (that is, be able to detect) covid and flu.
Nothing I’ve written is false, and nothing you’ve cited indicates anything nefarious on the part of the CDC, with regards to the PCR test. That is where my expertise lies and I think the scientists involved are doing good. The politicians on the other hand....