OpenAPI is useful because it not only generates a frontend for testing an API, it also can be used to generate the skeleton of an API's implementation. Can I generate Zephyr macros using this tool? Can I generate Android or iOS code? A complete tool should be able to generate firmware, Android, and iOS code for both a GATT server and client.
As a professional firmware engineer working in IoT, I'd advise against hanging your hat on Web Bluetooth. Bluetooth is already rife with security problems, and exposing direct control of it to a browser is asking for zero-day nightmares. This is beside the antipattern involved in asking web apps to directly control a peripheral's communication interface.