Recently, my MS advisor instructed me to submit a conference paper. They outlined what this paper would include, which would be a simulation study that is a near duplication of a ten-year-old published journal article (from a different group of researchers) that I have been reproducing results from for learning purposes. They said to omit citation of that journal article for the initial submission, and add it in the final draft if the conference paper is accepted. From a professional integrity standpoint, I have no intention to do this. I plan to write a paper that extends the results, and to include the citation in all drafts. I am unhappy that my advisor instructed me to essentially plagiarize, but plenty capable of not doing so, so I wasn't going to make a fuss about it.
However, in my literature search for writing my conference paper, I stumbled across Paper A that is extremely similar to one of my advisor's papers, Paper B. Paper A has different notation, but the same equations and results, published about 30 years earlier than my advisor's paper. Paper B does not cite this older paper, but does include a new simulation example in additional to the similar material, so it is not a complete copy. In light of their recent request to me, I am suspicious of my advisor's previous publications, and uncertain how to proceed working with them.
Should I show this older paper to them and ask about it? Should I report this to some higher authority? Is this a relatively common occurrence that I am overthinking? I do not rely on my advisor for funding, but I would not be thrilled about sabotaging my thesis by starting drama with my advisor. I would also not be thrilled to sabotage my future publishibility by working with a serial plagiarizer.