Hi, Is it necessary for moderators to write friendly private messages? Maybe you could add rule for moderators not to chat with users if they don't want? or give option to delete or hide message?
Here example how mod reacted to simple report about bot use on anilist:

mods are also people. Let them be casual, i like it better that way tbh. whats the problem
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you know what. i also think you should be able to delete mod messages on your profile, cuz they really irritate me too, but dont be that butthurt about it. Maybe @Maora is really nice
So some things.
"Maybe you could add rule for moderators not to chat with users if they don't want?" If a user explicitly makes this request then we typically honor it. However I do not believe you have made such a request. Even with such a request it doesn't mean you won't have interactions as they may reply to a status by another user that you are also in and other such things
The above message was still a mod duty, it was a mod thanking you for making a report.
We will not add an option to delete mod messages.
I highly recommend you seek out some counseling because its becoming more and more obvious that you have some issues you need to work out about persecution complexes.
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You can turn notifications on other persons message, so no problem with that. My sugestion simple to split mod profile messages to 2 types: Mod messages and Casual messages. Mod messages should be something what people can't ignore and casual stuff we could delete or simple block mod.
Theoretically sure, but its still not a big deal one way or the other
She didn't needed to use word "joke". The only way it could be ok, if she asked if i was joking or not, but in this situation the easiest way to check it if it's true, is simple by checking data yourself.
Simply put, no?
Keep your incompetence to yourself.
Remember how the other day you or your friends were editing mod messages to lie about what mods had said to you?
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Correcting users who make up false claims about mods is actually a mod duty as letting those go by uncontested may make passerby actually believe such which may negatively impact user and mod interactions.
You'll have to forgive me but I don't like it when people accuse me of things and threaten to call the police on me for those fraudulent claims. I don't care if its a joke one way or the other.