I've had gas water heaters re-located within mechanical rooms for better access and storage and that issue hasn't come up. (Not in Washington.)

Just give a call to a licensed local electrician (or gasfitter if the tank is gas-fired) and you'll get your answer.

Well, the water heater is electric (furnace is gas), but it sounds like you agree moving the water heater closer to the furnace shouldn't be a problem. As an adult I've mainly lived in condos, as a kid growing up in NJ in the 70s/80s, as I recall we had the water heater and furnace right next to each other, but of course codes and such change. I think there they were both gas. At one of the condos (NC), they actually were each in two separate locations, but I assumed that was an engineering decision based on where the outdoor part of the HVAC was. Again, both gas.

"Huh?"

Fixed.

Ditto!

I don't there is a code for a minimum distance. My gas furnace and hot water heater are 16 inches a part and the distance never came up when the final inspection was done on the furnace replacement.

How old is your hot water heater? If it is older than 10 years then you should consider replacing it with a gas fired model. Depending on your electric and gas rates you could save quite a bit on operating costs. You will have have a faster recovery and possibly go down a tank size.

Each appliance only has an access and maintenance distance around it. Other than than, determine layout like proximity to floor drain. And if you have a furnace <90% AFUE, the entire open basement was probably used to meet Combustion, Ventilation, and Dilution requirements for your gas burner. Closing in a mechanical room you would have to verify those if your furnace doesn't have other methods used.

You need to maintain service access around the furnace and water heater according to manufacturers' instructions. Mainly that's going to be in front of the furnace.

You have the square feet to install a hybrid electric water heater. I'm with Mike Home, if it's older than 10 years, consider a replacement - but I'd go with a hybrid electric and save a ton of money over standard electric. A gas water heater would require a flue that you don't have if you have a condensing furnace. There are ways around that (power-vent) but that makes no sense since you could just go with the hybrid electric.

Hybrid electric needs about 800 cf of air space. If you won't have that when you redo the room size, you can vent it to the adjoining room with a vent kit.

If you have the option for outside air intake on the furnace (PVC pipe), do that.