1) Assuming animals were a major source of variants, it quantitatively but not qualitatively changes the problem. Until we know the quantities, I do not see how you can assert relevance.
2) The references you provide say Omicron came most likely from a human with prolonged infection. The paper proposing a intermediate variant in mice is interesting, but considered unlikely (your reference: "Evolutionary biologist Mike Worobey, Ph.D., of the University of Arizona in Tucson, said the most plausible theory remained that Omicron evolved in an immune-compromised patient with a protracted [SARS-CoV-2] infection.")
Viral replications are the only scenario where variants can emerge naturally. Duration of disease and severity of disease are correlated with load and total viral replications. Vaccination reduces both at the population level. A vaccinated person therefore will on average be a less likely source of a variant. How much this weighs against other factors when deciding on policy is impossible for me say, but I would insist it is not irrelevant based upon current knowledge.