Noone is claiming symbiosis. Covid isn't symbiotic, it's pathogenic.
Influenza stays in the human population by a process known as antigenic drift. This means it changes slightly - just enough to stay ahead of the immune system but not so much that it becomes a new disease.If you have covid-19 you cannot live with it and it cannot live inside you for a long period of time. Either your body will kill it or it will kill you.
The common flu has a reservoir inside birds which are in regular contact with humans. It cannot live in us for long... But because the birds are right there they keep bringing it around each year.
Covid is mutating in a similar way - there are lots of strains now, with several in circulation that are of concern. If Covid continues to mutate like this, it will stay in the human population and just go round and round, just like influenza does. No need for birds or bats to keep the cycle going.
Seasonal flu is typically a combination of H1N1 and H3N2. H1N1 has been causing human deaths for at least 100 years being the cause of the 1918 pandemic. H3N2 caused the 1960s "Hong Kong flu" that killed over a million people.
Covid isn't influenza - they're not remotely related - but it is an example of how a virus can stay in the population at a much lower fatality rate. There are 4 corona viruses that cause some human common colds. They moved in to humans from other species. They don't need those other species to stay in the human population. They remain with us by antigenic drift. That's why you get the common cold year after year after year.
To think Covid will suddenly disappear is very hopeful but perhaps misguided.