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.
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.
It can work with any Swagger/OpenAPI spec AFAIK, does run on .NET though. Other than running it if you're just generating a TS client you don't need to be part of the .NET ecosystem at all.
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!
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.