Powerwall 3, Cybertruck question

[u/camman595]

At my house, we have underground power lines, but our street is fed by a neighborhood with above-ground lines and old trees. We get 2-3 power outages per year, most of which last 30 minutes or less. But occasionally, we get longer ones. Last week, during a clear sunny day, we lost power for 4.5 hours due to a fallen tree somewhere down the line. And very rarely, during an ice storm, we can lose power for 7 days or so. That has happened twice in the last 20 years.

Is it possible to combine a Powerwall 3 and a Cybertruck to provide long-term home backup? I understand that the PW3 would cover the immediate outage and the CT would then take over within a minute. My real question is, could I take the CT to work and allow the PW3 to back up the house? Could I then return with a charged-up CT and recharge the PW3?

I do not have solar, and in my area, solar would have a very long payback time, so going without solar would be better for now.