No. I want to state that from the top rather than keep you in suspense if you are worried about that. Now take a deep breath, relax and read on.
COVID 19 is often called corona virus. That is probably how the confusion started. There are many coronaviruses that impact humans, other species, or both. Corona viruses in people include the common cold, as well as other more severe infections https://www.who.int/westernpacific/health-topics/detail/coronavirus#:~:text=Coronaviruses%20(CoV)%20are%20a%20large,Syndrome%20(SARS%2DCoV).
Corona viruses in cats range from mild respiratory infections to FIP. Effective vaccines to protect cats from FIP have been studied for decades but are not yet available. Current vaccines are the traditional type, using killed or modified virus in serum. They do not provide enough protection from the most prevalent strains of the virus.
No mRNA vaccine exists yet for cats. However, a grant was awarded recently to begin research to develop one. https://www.morrisanimalfoundation.org/study/developing-mrna-vaccine-feline-infectious-peritonitis
Another virus in the coronavirus family is bovine Corona virus (BCV) that causes diarrhea in cows. Perhaps this is what led to the circulation of misinformation about cows receiving covid 19 vaccines. While there is a vaccine against bovine corona virus, it is an "old school" modified live virus vaccine. It is not an mRNA vaccine.
COVID 19 vaccine is not used on cows. There are currently no mRNA vaccine of any kind available that farmers could give to cows even if they wanted to.
Will there be mRNA vaccines for animals some day? Maybe. There is research being done. Will that be a good thing? Maybe. It depends the effectiveness and safety of the vaccine and on your point of view. If you value sustaining the lives of animals and reducing their suffering, a medical breakthrough that does that would be viewed in a favorable light.
With the advent of social media, anybody can publish anything and reach a worldwide audience. It is increasingly important to be able to identify authoritative sources, and to learn and use logic and critical reasoning skills. Unfortunately, these Increasingly important skills are not emphasized enough in public school curriculum or even at the college level. To help my own students navigate the world of information and misinformation, I found a link to a free course in logic and critical thinking that is similar to the one that I took in college decades ago before the Internet existed. This is the link I shared with my students: