Hi Max and welcome to the forum! We’d love to help you with your HomeAssistant integration, but we’re not quite ready.
The standard forecast API will NOT work the way you are using it. Access will be based on access token (personal or Oauth based) rather than (or in addition to) API key. And the forecast provided will be based on station_id rather than lat/long. An update to the documentation is coming soon, which will include more details on the access token concept as well as details on the forecast side of the API.
To get you started, check out this post: Oauth2 Access Token - #6 by dsj