No idea, I got into the shower after my wife and niece finished theirs, to find only cold water coming out of the pipe. Checked the app, and it showed the tank's hot water was empty. I would say 50 gallon is average, at least where I live. The previous tank installed before I bought the house (3 bed 2 bath) was a 40 gallon.
It may be a common tank size however such a tank is designed to have a permanent power supply, or at least have power available most of the time perhaps only avoiding peak electricity demand period, allowing the thermostat to control when reheating occurs.
It may have a second upper heating element with an upper thermostat on a permanent power supply being used to extend capacity and provide a quick reheat to the top portion of the tank so the wait for some hot water is significantly reduced.
If you want to operate a stored hot water supply on energy supplied for only shorter part(s) of a 24 hour cycle (e.g. from solar PV and/or from off-peak electricity), then it requires a larger tank. Heat when energy is cheap to be consumed throughout the day and night. Lather, rinse, repeat. There's really no downside to having a larger tank - you consume the same amount of hot water but you'll be less likely to run out at inconvenient times.
Increasing hot water delivery capacity without changing tank can be achieved by increasing the thermostat set point temperature. You don't shower in hotter water, you just end up using a bit less hot water and a bit more cold water to get the desired water temperature.
As a rough rule of thumb, each °F the set point temperature is raised increases the hot water supply capacity by 1%. So to gain 10% more hot water delivery capacity, lift the set point temperature by 10°F. Tanks should be able to safely heat/store water up to ~155°F or more but check the specifications.
Another solution is to reduce demand - low flow shower heads.
Another might be a washing machine which heats its own water and use that only when energy is cheap. That reduces demand on the limited hot water supply. Obviously uses the same amount of hot water overall but saves the tank for personal use. Same with washing dishes, good dishwashers heat their own water and are water efficient.
Not saying make changes immediately (other than low flow shower heads) but as/when the opportunity arises.
I actually have mine set to 122 (I just like that number) for the winter, and 125 for summer.
You mentioned you set yours to 122°/125° depending on season - is that the water heater's thermostat setting (the temperature inside the tank water is heated to), or a thermostatic mixing valve setting (the temperature from the hot water outlet which is mixed with some cold water)?
If the water heater's thermostat (water inside the tank) is set to 122-125° then setting the thermostat to 150° will add 25% or more to the hot water delivery capacity (another 13 gallons or so). It will consume a little bit more energy as daily heat losses will go up but you are less likely to run out of hot water.
My daughter is 4 now, soon it will be a 3-female household.
With young children (or the elderly/disabled), if you don't already have a thermostatic mixing valve then you should (at least for the bathroom hot water supply), especially if you choose to lift the thermostat set point inside the tank. That way the actual max temp of delivered hot water will not result in an immediate and permanent burn/scalding injury.
I swear, sometimes I'd have to pee outside because both bathrooms are occupied. No having to do a number 2 out there yet, knock on wood!
