The inverter plugged into a most powerful socket in cali (20amps behind left seat) will handle 240watts max (on paper..)
The socket design is pretty flawed and hardly holds 10amps 120watts for prolonged uses without overheating.
You will have to connect the inverter to the battery directly, which isn't for all.
The important thing to understand that most appliances don't use 240v directly. For example, laptops are usually 19volts. So converting 12v to 240v and then 240 to 19 with power supply is a huge waste.
You can find or make 12v power supplies for most devices by using voltage up-stepper.
Another thing to understand is power. You can read power consumption on most appliances for example 2200watts for the electric kettle. Which you can forget using in a van
Even a lithium battery I am currently installing to California which is equivalent to around 3-4 cali leisure batteries put together will power such cattle for just 30-35 mins.
P.S. in short don't expect to power anything higher than 100-200 watts for prolonged times.
We use two 100watts slow cookers and 120watts thermos teapot that cover most of our travel cooking needs. Two2 50l freezers 50-90watts each. Laptop charger 90watts.
Off-grid means understanding each small part consumption and conserving energy.