Did you include the ClientID in the header?
Example from docs
curl -H "Authorization: Bearer eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJleHAiOjE1MDMzNDM5NDcsInVzZXJfaWQiOiIyNzQxOTAxMSIsImNoYW5uZWxfaWQiOiIyNzQxOTAxMSIsInJvbGUiOiJleHRlcm5hbCIsInB1YnN1Yl9wZXJtcyI6eyJzZW5kIjpbIioiXX19.TiDAzrq58XczdymAozwsdVilRkjr9KN8C0pCv7px-FM" \
-H "Client-Id: pxifeyz7vxk9v6yb202nq4cwsnsp1t" \
-H "Content-Type: application/json" \
-d '{"content_type":"application/json", "message":"{\"foo\":\"bar\"}", "targets":["broadcast"]}' \
-X POST https://api.twitch.tv/extensions/message/27419011
You need the ClientID, Content Type, and the Auth headers as documented