Making friends in academia and building connections
I don't know if this is much of an answer, but it's become more than will fit in a comment.
If you just joined in Fall 2020, it's not unusual that you haven't made the kind of connections you're looking for yet, especially given the challenges of the pandemic. I'm a PhD student, and I'm sure it's very different for faculty than for students, but I'm not fresh out of undergrad and have been through a couple career transitions prior to grad school. In my experience it takes a year minimum—even in the best of conditions—to organically develop relationships with coworkers/colleagues. (It took me longer than that to build close friendships with folks in my cohort, and we had weekly, in-person classes together for a year.) Genuine connections with coworkers tend to accrue in small increments over that time, and almost always in the interstices between &quot;official&quot; work demands. It sounds like you're fully aware of all this, but an occasional reminder doesn't hurt.
As you mention, everyone is exhausted these days. Perhaps your colleagues are all on the introverted side, but it doesn't sound like this situation has much to do with their feelings about you specifically. If they'd all been actively avoiding you or unfriendly, that would be a different story (and this is not the story you imply, at least, when you say your efforts &quot;haven't worked so far&quot;). Your colleagues may also be trying to give you space to address (or not feel close enough to engage with you about) your family health issues.
In any case, the window is far from closed. I'm still friends, a decade later, with some former colleagues who barely even spoke to me for the first few years at my previous workplace. And although I'm obviously not a super outgoing make-friends-easily type of person, my sense is that that sort of experience isn't unusual.