BTW, a "true-sine" backup battery will keep your home network up. I have unit from CyberPower that works well. $120 or so.
I have had no issues in 4 power outages with our network remaining up.
The PowerWalls have worked quite well for us.
I appreciate the advice, but it's (probably) a more complicated issue than you think it is, and this has been a well-traveled and well-understood, yet frustrating, path for a number of Powerwall owners. It has to do with the AC line frequency and interactions between the Powerwalls, solar inverter, and commonly-available UPSs. Rather than try to explain it (which I probably would do poorly), I'm just going to point to the thread in the Tesla Energy forum where this has been discussed at length.
Powerwall 2 + UPS Connundrum - and solution
I owe that thread an update on some things I learned over the past few days.
Thanks,
Bruce.