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.