How can data subjects exercise their rights to restriction and to object?

How can any user know the controls in place to restrict and object to the processing of their data given to the AI platform?

You have the below features to exercise the rights for data protection. Please take a look at these and use them as per your use case.

PII feature - (Note this is targeted for personally identifiable information - Not all sensitive information like password are PII. So, they need to follow a very tight pattern/regular expression for the PII engine to identify any input as PII and obfuscate/mask it)
Data retention policy (at an account level) -
Delete customer data API (chat transcripts only - NOT bot etc [a developer is not being considered an end-user here]) -