Regarding the idea of powering your home in a power outage (which happens here frequently), how long could a vehicle actually power a few appliances before running out of juice, which would also strand you at home with no way to charge your vehicle? I'm new to the EV world and have a lot to learn!
As others have said, how long the EV can provide power depends on the load and state of charge when the power goes out. But if you are curious, you can search YouTube - I have seen a few videos of people using their EVs to provide power during an outage. They usually say what they powered and how many days the EV battery lasted. I own a Ioniq 5, so of course I'm going to recommend the emergency backup power video by The Ioniq Guy.
Spoiler alert - he calculated 5 days of backup power using the Ioniq 5.

But to answer your other concern: "strand you at home with no way to charge your vehicle" - this will not happen. All BEVs that I know about with V2L (Vehicle 2 Load) have a minimum power setting. My car's minimum setting is 20%. That means the car will stop providing power when the battery reaches 20% charge. I can change that to a higher value if needed. I have not changed it because if I am using the V2L for power during an outage, 20% is more than enough range to drive to one of the DC fast chargers in my area so I can recharge the battery in the car.