For peers at same level in their own setting that is indeed true. When with people that report to you, might not be a good idea because, one can't tell if even the laughter is genuine or obligated to.

There are some instances where it might potentially help - when your team is under stress (real or perceived). Light humor (if well done), might alleviate some of the tension in the room and let them focus on work.

As management especially, joke clearly. There is far more weight on you to not mislead than for the "keep a serious atmosphere" that some might take it as

You have to be careful. Relationships sour, and nothing is funny when read in court.

One thing is for certain, NEVER put jokes or sarcasm in writing.

I've read way too many of those in court.

Many ordinary social interactions have become sins recently. Saying anything that could be interpreted as offensive poses a very real risk to your career, the list of potentially offensive things is incredibly long, and gets longer with each passing moment as novel outrages pop up in all corners of the world.

You can still be kind, empathetic and polite to everybody you work with. But avoiding authentic personal relationships at work is very sensible, along with having very clear personal boundaries. Normal colleagues can form cliques of people they trust, but it’s not a great outcome for management to be participating in that, even though that’s what usually happens.

But inappropriate jokes about firing people and the like are not "ordinary social interactions" with aspects "that could be interpreted as offensive", they are an objectively oppressive and distressing behaviour that even the least upset subordinates of such a manager recognize as inappropriate.

I’d agree that this is usually true. But the comment I was replying to is about jokes in general.

I don’t know why this is being downvoted - it’s good advice. You should adopt a “work persona” that elides the riskier elements of your true self.

“Bring your true self to work” and other modern workplace nonsense is risky advice to take seriously. It’s mostly a coded communication that does not mean what it appears to on the surface.