General

Heat pump is 3x as efficient as electric heat.
Point of use is 27-50% more efficient than tank water heater [1]
Electric is 2x as efficient as gas - this one says 74% vs 40% efficient.
induction is 20-25% more efficient than electric cooking - with induction at 90% and electric at 65-70% - [2].
Electric water heaters (tank) are about 95% efficient, while gas are about 63% efficient [3]
Efficiency factor (EF) considers standby loss but not distribution loss. Gas is 60% and electric is 90%. Tankless gets gas EF up to 82% (standby efficiency), but that doesn't consider distribution loss. Electric is 100% efficient to begin with, so standby would be near perfect efficiency. If you are at the point of use - you are close to 100% efficiency.

Standby Losses

Standby losses for water heaters are about 1000BTU/hr - [4] - or about 300W!
1993 average was 1200kWhr/year! [5]. Equivalent to 140W. That is more reasonable.

Electricity costs about 2x as much as gas for the thermal content - but it's lower cost if you use a heat pump.

Shower x2.5 - 6 minutes - 15 minutes
Dishwasher - 3 times per week - or 3/7* per day - of 4.5 gallons - with 0.3 gpm water use - 15 minutes of how water at low flow. But only about 7 minutes of that.
Washing hands and brushng teeth - 6 minutes *2.5 - 15 minutes
Total - 37 minutes of hot water - or 1 kWhr with a 1.6 kW water heater.

Point: there is absolutely no case for gas heat with advances in heat pumps! Unless you are attracted to having a gas system in your house for some other reason. One advantage is that gas can be available even if electric dies - so gas is useful from a backup perspective. But backup heat is done better via pellet stove - cheaper and more decent(ralized).
There is little case for gas water heater with point of use electric heaters! Which can be as efficient - as they save both standby
On-demand heaters, when used with low flow - can easily use less energy than tank heaters lose in standby! In fact, we are using 1kWhr - 1/3 the very loss of tanked heaters!

While impossible to track in a dumb home, a smart home system can control all energy use automatically.

Reduce flow of water at night to conserve on heating energy
Turn off all parasitic loads: turn off all circuits outside of internet/computer/lights at night.
Keep devices off - such as bathroom water heater - until you walk into the room.
Switch power to a specific room off when you leave the room
Don't use any devices that have parasitic loads - or turn them off at night.
Possibly use relays at breaker panel to time circuit turnoff.