If you're determined to turn this issue into a battle of self worth between "good IT people" and "bad IT people" I can foresee that you're going to lose this well paid job in a really obvious and predictable way. Given that they pay well, why would they waste their energy fighting with a developer when they can just get a new developer with similar skills that's willing to work with them?
My issue is more when the response to a new piece of minor technology that will make our lives easily is: "I don't want to learn YAML".
Which is fair, and I'd give the same response, I don't want to learn YAML either. In fact YAML seems to be a perfect example to use. In the beginning was XML, and XML sucked. For many, many reasons. Then we got JSON, JSON fulfills a similar function to XML but is much better in basically every single way. YAML is not better than JSON, but it is one additional thing that now exists. That describes a lot of new tech, "it's not better than 'x', but it does exist", and once implemented, will have to be maintained forever.
I mean, you probably could persuade your senior about composer and OpenAPI with the right approach, but if you're determined to turn it into a struggle it stops being about the technology. I hope you didn't say "You need to improve, every day." to their face, because at that point you've basically insulted them and they would seriously start questioning if your skills (which you have yet to prove) are worth the hassle of dealing with that every day.
You should consider, is this about the technology, or is it about your image as a "programmer" and wanting to always align with the mental image of being a "good developer".