The Lancet study shows that there is trace amount of the vaccine mRNA in breast milk, presumably the study takes no position on whether that is a "safety" issue (otherwise it would have been bigger news and Public would have cited that part).
Given the above, the Lancet study does not support that claim that the CDC "lied about safety" even if the CDC "had repeatedly assured pregnant and breastfeeding women that it was safe to get vaccinated."
But the fact that it IS there should not have been censored by Meta.
Had Public's claim been limited to stating that trace amounts of mRNA is there in breast milk, that would have been an accurate restatement of the Lancet study's finding; but Public went outside of accurately restating the study's finding and went into the territory of accusing a public health agency of "lying" about "safety" -- this is not supported by the Lancet study. This went beyond citing a study and got into sensationalism and scare mongering. For that, I have to sympathy for Public's article being limited by Meta/Facebook. (Show me that the Lancet study says that the trace amount of mRNA in breast milk is unsafe and I am ready to change my mind on this.)
Facebook/Meta is a private platform/enterprise. If you don't like Facebook/Meta, go post your stuff somewhere else (like, say, Substack). Facebook/Meta owes Public no duty to carry or promote any of Public's posts or articles.