Telegram – How to Auto-Sync Supergroup Users to Channel

I don't think there's an existing way of doing that, but maybe it can be achieved via the API.

Note: I heard of people that added multiple users to channels and then got banned/restricted in some way or another. I don't know (and couldn't find out) what are the limitations before it would happen.

I think that the most probable way is to use the Telegram API to achieve that, maybe by creating a little script/app that will read the users from your group and add them to the channel.
Have a look at the messages.addChatUser method.

A question on StackOverflow that asks how to do it with a bot:

• Add user to channel automatically when user asks

If you don't want to risk anything (such as being restricted), I would go by engaging users to join by themselves:

• Create a nice post with an image an a button to the new related channel.
• Forward messages from the channel to the group.
• Pin an invitation message to the chat (assuming you're the admin).

Note that if you're not the admin, they will probably won't be happy with your advertising..