It's not a gentle push though. It's setting up a group pressure situation that is definitely gonna make introverts feel uncomfortable (by a probably extroverted person that may genuinely not understand what they're even doing in that regard as it'd feel natural for them).
Now I understand that with remote work there may not be enough space for chit chat. But there are other ways than a forced group pressure situation to set that up.
For example, we decided as a team when Covid WFH started to basically use our daily 15 min stand-up for whatever. Sometimes we just did stand-up and we're out of there after 5 min coz nobody felt like talking. Sometimes it'd be a half an hour of just talking about whatever. We also have a dedicated time each week blocked off on the calendar for it as well and when we have ad hoc working session calls we get in some chit chat here or there as well. It's not all just business but it can be.
RE cat: see this is the internet and it's an anonymous forum. I used that example because our cat actually just died a few weeks ago. You thought it was over the top. Interesting indeed.
I thought feeling compelled to make up a story like a dead cat would be over the top, I'm so sorry that actually happened.
I don't quite get the difference between a blocked off time for chit chat and the way the manager asked for it here but totally, being forced like you have to say something you don't want to sucks.
Feeling compelled to make up a story is part of the whole group pressure thing. Either you overshare i.e. share something that actually happened but that you would never have wanted to share without the group (and boss) pressure situation or you make something up (like many people in the comments here are saying).
I guess the difference is the same what I mentioned about stand-up changing: The team decided to do that. It wasn't a manager saying that's how we do things now.
EDIT: I also just realized you gave out condolences. See if I was in the situation from the article I might not be able to quickly come up with something fake and I'd instinctively just mention the cat thing (coz I don't want to be the guy that gets shunned). And then the next few weeks are gonna be very uncomfortable coz people will keep mentioning it.
Now I understand that with remote work there may not be enough space for chit chat. But there are other ways than a forced group pressure situation to set that up.
For example, we decided as a team when Covid WFH started to basically use our daily 15 min stand-up for whatever. Sometimes we just did stand-up and we're out of there after 5 min coz nobody felt like talking. Sometimes it'd be a half an hour of just talking about whatever. We also have a dedicated time each week blocked off on the calendar for it as well and when we have ad hoc working session calls we get in some chit chat here or there as well. It's not all just business but it can be.
RE cat: see this is the internet and it's an anonymous forum. I used that example because our cat actually just died a few weeks ago. You thought it was over the top. Interesting indeed.