You can look in Pub Med. Beta Glucan is the active ingredient in these mushrooms. In order to narrow the search, you can use the term ‘immunogenicity of beta glucan’. also search for elderberry to see research articles.

Probiotics are probably helpful in restoring a depleted gut flora but of no use whatever in fighting off a virus to which we have zero immunity. Bacteria do not ‘compete’ with viruses for food in the gut or anywhere else for that matter. Viruses attack cells in the body. In the case of covid-19 the cells of the respiratory tract. There is no defence other than robust good health (and a strong immune system) and avoiding getting infected in the first place.
There is no evidence that L-lysine or zinc ‘nullifies reproduction and multiplication’ of any virus.
This kind of ill-informed pseudoscience is at best a waste of time and money and at worst downright dangerous.