You need to use CLI on your machine indeed, you sign in with your credentials, you write and deploy your Edge Function. After that you can use the Supabase SDK instance which WeWeb (not officially) provided (this is soon gonna be deprecated for a newer version 2).
I think here you can find the exposed instance of supabase to use to trigger the Supabase Javascript Client - Invokes a Supabase Edge Function. but I’m not sure whether you can use this feature this way, might be a question for @Alexis