There are two completely different issues here, a bot having reputation and the associated privileges, and a bot voting in a problematic fashion.
I don't see any issue with the first part, the bot account earned the reputation the regular way, I assume. The owner used the second account to earn reputation, and as long as they didn't cheat in any way, this is perfectly acceptable. Giving a bot that access is not an issue either, though the user is still responsible for any actions the bot performs. If the bot messes up, the bot account can get suspended or deleted as a consequence.
In cases where any damage was caused accidentally, that's probably all that might happen. If a user is negligent or reckless with his bot, the main user might feel some consequences as well.
The voting issue is a separate concern. I'm not sure if there is a rule, but I'd consider any voting done programmatically by a bot and not controlled by a human to be abusive and reason for removal of the bot account.
The bot account itself is just a sock puppet, it's bound by all the rules around sock puppets. So it is not necessarily against the rules to use that account to vote (controlled by an actual human), but it is likely a bad idea and could easily violate the rules e.g. by voting on the same post with the bot and the main account.
I don't think the bot aspect changes anything here, those accounts are simply sock puppets. We already have rules for them, and tools to investigate and deal with them if they violate the rules.