As BGbreeder says, it all depends. If you really want a very specific answer. You'll have to do the legwork.
There are myriad home energy monitors that allow you to see your actual energy usage at an appliance or circuit level. Once you know what you will back up, you can determine how much energy those backed up items take per day, then calculate how many days of backup one ~13 kWh battery can provide you.
I posted about one option here, but there are others.
I have been using Emporia vue for past few months now and love it. SCE also gave a $25 rebate for it. Once I found how much the dish heater from Costco consumes, I sold it the next day.
teslamotorsclub.com
For example, let's pretend the circuits that run the core household loads (refrigerator, bedrooms, living rooms, and extra refrigerators) consume an average 6 kWh per day. So with this logic, if you knew there was a power outage (and had zero solar production), one Powerwall could theoretically provide about 2 days of backup if you only focused on your core living needs.
And if you just sat in your house doing nothing but keeping your food from spoiling, you could maybe get a week of backup.
And on the other extreme, if you cook with electric, heat with electric, have air conditioning, and turned on a pool pump... you could wipe out this one battery in 2 hours.
That's why nobody can tell you how long a battery will last you. The battery just gives you some storage (which decays up to 30% over the useful life). It's up to you to figure out how long that storage can last.
For my specific house, I have 3 Powerwalls that give me about 39 kWh of stored energy potential. It turned out that in 2021 on the hottest day of the year when the air conditioners are running as hard as possible, my house pounded through 38 kWh of electricity from 3pm to midnight (9 hours).
So, my shortest backup is 9 hours. And on the other extreme... if I have solar production + aggressive load shedding, the 3 batteries could conceivably last an entire year.