> the term historically existed (AIUI) to denote regions that the researcher found to have phenotypic relevance
That's Mendelian genetics. Geneticists focused on DNA as a physical molecule rather than a conceptual unit of inheritance use the same word to refer to a region of DNA that produces a protein.
They're both important concepts, but they're not the same concept.
Okay I got the terms wrong but I think the core point stands: a gene is typically defined with respect to some research objective and area of interest, and is highly variable depending on what you're looking at. It doesn't (yet, at least) have a natural boundary. People looking at one phenomenon might see one boundary for a a gene, while others see another.
In fact, I think that term is great for comparison: "phenomenon". Asking for the "minimum genes for viable life" seems like asking for the "minimum number of natural phenomena to put a man on the moon". Are those two phenomena really just different manifestations of "gravity" or are they two things in their own right? "It depends."
Arguably, the production of a protein is nearly the smallest element of the observable characteristic of an organism produced by the interaction of its genotype with the environment, and thus sort of the fundamental unit of phenotype, so, from that perspective, they are exactly the same thing.
They are not the same thing from any useful perspective. You can remove a (protein-coding) gene, or replace it, without altering the phenotype at all. You can make changes outside protein-coding regions and get large phenotypic changes.
That's Mendelian genetics. Geneticists focused on DNA as a physical molecule rather than a conceptual unit of inheritance use the same word to refer to a region of DNA that produces a protein.
They're both important concepts, but they're not the same concept.