This is just wrong. Vastly more tests were done for the flu during the covid pandemic than have ever been done.
Source: https://www.nytimes.com/interactive/2021/04/22/science/flu-s...
My wife is also an ER doctor and agrees that there were times that they didn't perform many/any flu tests--mostly in the spring of 2020 and after none of the flu tests were returning positive for a while. But this past winter people have definitely been tested for the flu. Rapid influenza tests are also usually performed first, only sending to labs when confirmatory testing is desired.