It seems like a backwards way of doing things, but if I understand what you want to accomplish right, the way to go about it would be for each of the ‘bots’ that want to use your account have an auth page, where you would log into your bot account and then go through each bots OAuth process to grant them a token for your bot account.
OAuth tokens are private, so shouldn’t be shared. If you was to share a token and one of the bots gets compromised (or a user is intentionally malicious), and the token gets out in the open then you’re account is liable and you would need to revoke access to everyone. When done properly (as much as anything in this setup could be considered ‘proper’) each bot would have their own token to your account so you can revoke access specifically where needed.
Also, StreamLabs chat bot isn’t breaking the ToS as no username/passwords are shared, just permissions granted through the OAuth system which is fine by the ToS.