Swagger, OpenAPI have nothing to do with REST. In fact, they are the antithesis of REST, because they are the very out of band information that a REST client is

Swagger, OpenAPI have nothing to do with REST. In fact, they are the antithesis of REST, because they are the very out of band information that a REST client isn't allowed to depend on. A REST client for a pizza delivery restaurant isn't allowed to know that the "order" action is called "order", because that is out of band information. If the server is replaced by a hotel booking server with a completely different workflow, the client is supposed to continue working. Only MCP is loosely related to REST and it's because one of the defining characteristics of REST is that the API can be discovered at runtime, which is useful if you have a pseudo human level intelligence such as an LLM, but not if you have a dumb static application that has finite capabilities.