Again, they're independent variables.
WHO sites keep consistent testing for patients with respiratory symptoms. The same way that some flu cases may be "hidden" because people stay at home, likewise some flus that wouldn't be tested otherwise will because the patient thinks it's covid.
In any case if some hide because there's a pandemic or WW3, it doesn't matter because other patients will be part of the sample. If there's flu it will be seen, pandemic ongoing or not.
You may be interested in reading the Global Influenza Surveillance Manual[0]. Relevant info is in chapter 6, regarding sampling, in particular 6.2, in which it recommends against testing all and only those that seek medical assistance.
> Ad hoc or convenience sampling
> Sampling schemes that do not adhere to a pre-determined system are the easiest and least costly to implement but are also the most subject to bias. Differences in the health- seeking behavior of different groups and preconceived ideas about the risk of health- care providers can introduce unpredictable biases, consequently yielding patterns in the data that do not represent reality. While this approach may still yield data sufficient to identify transmission seasonality, and provide specimens for virological surveillance, it will not provide a reliable picture of the epidemiological characteristics of influenza or burden and should not be used if these are the objectives of the system.
In 6.4 it describes the systematic sampling strategies recommended, which remove the bias of the point you (and the other commenter) raised.
As described in 6.3, random sampling would be best, but also too expensive for tracking, and is only to be done by WHO sites performing some research where it would be needed.
https://www.who.int/influenza/resources/documents/INFSURVMAN...