I found the page that you took a picture of:This may be a reason why there seems to be a war on chickens. The egg yolk protects against covid and neutralizes the covid vaccines spike protein.
https://pubmed.ncbi.nlm.nih.gov/33191178/
And then I followed a link that said "free full text" to here:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7608017/
Looking through the full text, several paragraphs down, I find:
"Here, we purified anti-spike-S1 IgYs from hens that were immunized with the S1 domain of the SARS-CoV-2 spike protein and interrogated their ability to neutralize SARS-CoV-2 pseudovirus using Hela cells with overexpressed human ACE2. In addition, we used competition ELISA assays to validate the IgY’s competitive binding to various SARS-CoV-2 Spike protein mutants, as well as the SARS-CoV Spike protein."
A key phrase would be "hens that were immunized with..."
This would not apply to eggs from any other hens.
The section titled "preparation" has a few more details, including:
"Each hen was injected (intramuscular) with 150 μg of the recombinant spike protein under the wings, once a week for 4 weeks,"
Again, not something that is happening to most chickens.
I was able to get access without payingI am sure in the full article in the methods section it would have described how they infected the eggs, but I didn't pay to get access.

Edit to add:
Here is another page that appears to have the exact same study writeup, also free at present. (Same title, same authors, same text about how they did it.)
https://www.sciencedirect.com/science/article/pii/S1567576920336390