Thinking of this reply for a bit. From "How to survive a pandemic" by Dr. Greger, I recall this being an avian flu. So it's possible for covid to bounce around in them. Quick search, I'm seeing articles about even newer coronaviruses being discovered in birds. I don't think the wild population is the threat to most worry about creating future variants of covid. The biggest threat is probably where there are the biggest populations of birds in close quarters with one another and humans - on farms. Given how mink farms were recently slaughtered to stop the spread of covid amongst them, similar measures would be taken with poultry.
Avian viruses on farms have always been a big concern among the epidemiologists, if Dr Greger's book is any indication. Stopping the virus movements among humans and similar mass slaughterings among livestock could work. I takeaway that it's a statistics problem as to when and not if we see another virus capable of becoming a serious pandemic again.
The extent to which society learned how to monitor and react to new viruses during the covid-19 pandemic may well determine our fates next time.