Send a message on telegram: "Forbidden: bot is not a member of the supergroup chat" or "Forbidden: bot is not a member of the channel chat" – Telegram API

I am trying to send a message on a chat on telegram.
I want telegram setups to be done only with the official UI as I want it to be possibly done by by an end user.

Here are telegram setup I do:

• I created the bot XXXXXXX_bot with Botfather by getting the token: no problem
• I created a Channel:
  • click "new channel"
  • channel name: TestChannel
  • click "Next"
  • select "Private channel"
  • click "Save"
  • Add my bot XXXXXXX_bot
  • Click "Make admin"
  • Click "Save"
• I create the chat:
  • open the channel TestChannel
  • on the channel menu, select "Manage Channel"
  • click on "Add a group" in the discussion
  • click on "Create a new group"
  • group name: TestChannelChat
  • click "Create"
  • click "Save"
• I add the bot to the new group:
  • open the group TestChannelChat
  • on the right panel, I click "add member"
  • Add my bot XXXXXXX_bot
  • click "Add"
  • right click on the newly added user in the chat and select "Promote to admin"
  • click "Save"

Here is the setup of admins of the channel:

At the end of the day, the setup of the chat/group is the following in the telegram UI:

I make the following http call :

GET https://api.telegram.org/botXXXXXXTOKENXXXXXXX/sendMessage?chat_id=@TestChannelChat&text=coucou

that gives me the following answer:

{
  "ok": false,
  "error_code": 403,
  "description": "Forbidden: bot is not a member of the supergroup chat"
}

I also made the following (to bypass the actual chat and directly publish a message in the channel):

GET https://api.telegram.org/botXXXXXXTOKENXXXXXXX/sendMessage?chat_id=@TestChannel&text=coucou

that gives me the following answer:

{
  "ok": false,
  "error_code": 403,
  "description": "Forbidden: bot is not a member of the channel chat"
}

One simple question, as a bot is also meant to broadcast messages, what part of its setup am I missing?