There are a number of red flags here. 'We can't know about problems if you don't tell us about them' is bullshit. It is not on the employees to ensure that people don't get harassed or mistreated.
The 'sorry we have to be corporate' at the start is also problematic. Dealing with toxic work culture is not 'boring corporate stuff' and leadership should not make that suggestion.
The whole thing feels like a teacher reprimanding a bunch of unruly teens about classroom drama. Which seems misguided at best. If your company is infested with gossip, badmouthing and harassment, it's not because you happened to hire all the gossipy people, it's because you're creating a bad work culture that reinforces that kind of behavior, and you need to address that instead of blaming the people who work for you. Managers don't go around berating colleagues for the heck of it, they do it because it is accepted normalized behavior. And that starts from the top.