I don't see anything wrong with any of it.
1) It's a public sim. IRL as in SL you have little expectation of privacy in public, which is why every day you're recorded by any number of cameras from security cameras to accidentally photobombing someone else's picture or video without you even knowing about it.
2) It's local chat. It's basically the equivalent of you talking to someone on a street corner or crowded bus or something where what you say may be picked up by a security camera or even someone nearby completely within their own rights talking on the phone
3) The public sim is pretty much like any number of stores or businesses you might walk into on any given day. They are completely within their rights to record what goes on inside their store. Many of those security cameras are becoming equipped with sound recording capabilities too.
4) Your chat logs are being saved anyway. By you and anyone else in the sim who has the option enabled.
Are you going to get mad at the person next to you on a bus that's on the phone because your conversation is being heard by the person on the other end of the call?
Are you going to sue your neighbor because they installed a Ring style doorbell with a camera in it, and you happened to be walking your dog as the pizza delivery guy rang their doorbell? Or that a stray cat ran across their lawn, activating their motion activated security camera, as you happened to be walking down the street.
I'm all for privacy, but privacy has its limits. Especially in public settings. I see the chat logs as I would any security camera. It's for my protection as much as it is for theirs. If something happened and I was accused, you can look back at the logs and determine what really happened. Since it's a bot automatically posting the logs to discord, it would be reasonable to assume that the logs have not been tampered with.