Earlier quoted context omitted.
I've had success with NSwag for generating both TypeScript and C# clients. Highly customisable - maybe too customisable with the config being quite complex - there's CLI & GUI tools to generate configs though. https://github.com/RicoSuter/NSwag We use the C# client generator in our public sector project and package the results up within Nuget, works a treat.
Yeah Nswag is great, but pretty specific to the .NET ecosystem if i understand correctly ? Ideally we'd like this to become a universal generator where any dev/team/company publishing an API gets typed and idiomatic clients, including the long tail of languages.
But I like your idea of the universal generator. NSwag isn't the most friendly of things to configure & regenerate so something like your lovely site will make it easier for people. Best of luck with the project!