Authentication: https://dev.twitch.tv/docs/authentication/getting-tokens-oauth/#oauth-authorization-code-flow
Ingests: https://dev.twitch.tv/docs/v5/reference/ingests/
Get stream key: https://dev.twitch.tv/docs/v5/reference/channels/#get-channel
Sending data to that endpoint is just an RTMP connection, which you can do through ffmpeg directly or a library/app of your choice to handle that.