That's exactly the thing. Don't make it about you! How much of telling employee "this is bullshit, I could't sleep over this" is actually doing for them? Vs absolving yourself of guilt, having them like you, and making you look like the victim you definitely aren't?

Respect and support and empathy and sincerity are the key, always. Deflecting blame and ranting are not long term helpful.

The proper responsibility of a concerned manager in this case is to make sure the person knows you have their back in terms of future references, petty resources (one guy I knew was on the hook for >$300 in reimbursements when laid off, as far as I know he never got them - another guy was forbidden to take his personal mouse/keyboard home with him), and similar things.

If a mid-level manager actually cares, and was any good at their job, the best thing they can do is to keep doing it for that person.

It isn't doing anything for them. But it is sincere (I didn't say this in my post, but the idea is that my father actually did lose weeks of sleep over this). It, of course, should not be about you in this moment (this is hard to convey in a short post). But it seems far more supportive and honest than pretending that everything is okay and normal or acting like a robot.

Maybe it is also bad. I don't know. But the fake smile seems much worse.

Absolutely this. It was my misfortune to lay off teams of 20+ 3 times. You are the instrument. In that moment, they will want to hate you and you shouldn't try to deflect it. Do everything you can constructively behind the scenes to improve the situation before and after the announcement but, in that moment, it's not about you.