They do not violate the code of conduct
Seriously. Read through it. There's no part of it saying they aren't allowed. There isn't in the ToS either.
If you say keeping comments around is not nice, then by definition, the site isn't nice. Deleted posts, comments, and chat messages are still around. Only 10k users and mods can see deleted posts, only mods can see deleted comments, and ROs and mods can see deleted chat messages. They're still technically open, as anyone who can see it could theoretically share it with someone else who can't.
Also, the comments are public until deleted. Anyone could see them before that happens. As far as I know, moderators can see deleted comments.
A moderator has various bots that capture a bunch of comments, and these comments land up in various rooms that are in plain view of the community. I think this tactic is creepy surveillance and violates the CoC; it's not nice to keep everyone's comments on record, and then let other people (especially non-moderators) in chatrooms bring up the comments again and again for discussion, causing more and more unnecessary and unwanted drama.
There are tons of moderation bots. There are fewer for comments, and some delete the comments, others don't. It's not surveillance though. If you post something on the site, it doesn't take long before web crawlers find them. Some even go into web archives.
As for bots, I personally don't see a problem with them. They aid in moderation to keep unfriendly/chatty/otherwise unwanted comments off the site. For an instance, Queen (SOBotics bot) does this. Interpersonal.SE has a bot too, which also is designed to help with moderation. And it's also worth remembering that everything you post on SE (questions, answers, comments, chat messages), are licensed under CC by-sa 3, which means anyone can do anything with it, as long as there's attribution.
To be honest, Journeyman Geek sums it up pretty good in their answer:
All of these comments are public. This is roughly about as creepy as sitting at a café commenting on the cars passing by.
Also, it's not just mods creating bots. There are regular users who create them as well. I'm guessing SE has some private bots as well.
This is particularly important when some users may post comments that they subsequently wish to delete shortly after. Some things in the comments are said in the moment, some things are said but meant to be transient and not meant to be logged permanently in plain view of the community.
If a user wants to keep something private, they shouldn't post it in the first place. Posting something, and deleting it, to keep something hidden is usually not allowed. The exception is for accidental posting PII. But if someone posts a rude comment, and then deletes it to not get caught, that's technically abuse of the system. The same applies in chat. But it doesn't necessarily have to be rude, it could be something they want to keep private for other reasons. In which case, it's still not a good idea posting it. The API catches it up, moderators can still see it, and users can read it before it's deleted.
I do agree, there are things you might wanna remove (i.e. accidentally posted PII. Happens sometimes, when i.e. an asker forgets to remove an API key or hide a username and password, or IP, or something else), but most bots don't pick those up.
If moderators with diamonds and the higher ups, e.g. Stack Exchange staff members already have access to pretty much every piece of information that is around the network, the least they could do is to keep deleted comments away from public view -- they are deleted by users for probably good reasons.
They're still accessible through the API before deletion. Even if there is a good reason for deletion, why should it be hidden? Anyone could technically keep a full store of all the comments on SE, and post them. It wouldn't be a problem as long as it's attributed (and doesn't otherwise violate the license).
Do you think these bots are problematic?
No! In fact, they're the opposite. Bot assisted moderation has helped a ton, especially with comment moderation. There aren't a lot of good tools for finding them automatically (like search). Charcoal has a tool that creates a real-time feed of comments. SOBotics has a bot too. Some sites, such as Interpersonal.SE, have their own bots. They're all created for use on different sites, but they still help with comment moderation.
Can we put an end to that practice or at least fix the way in which this creepy surveillance is being implemented?
This isn't surveillance. It simply creates a copy of a comment somewhere else. If you worry about comments sticking around somewhere, you shouldn't post it in the first place.
Also, it's highly likely your comment(s) have been picked up by search engine caches already. These are also available to everyone.