I recently installed a new electric water heater and now I only get hot water to one faucet at a time. The kitchen faucet is closest to the heater with the bathrooms being the furthest. when i turn on the hot water to the kitchen faucet i get cold water til i go to the bathroom and turn on the hot water there then the kitchen turns instantly hot while the bathrooms only get warm water. haven't been able to get hot water to the bathrooms at all, only warm.
When this happened at my house it was the antiscalding valve at the water heater. These mix cold and hot water together to reduce the temperature of the hot water to safe levels. Some places install them at each faucet, others install them at the water heater itself.
Turning on one faucet would just give cold water no longer how long it ran. But opening others, or sometimes turning the tap on and off rapidly a few times would bring the hot water.
The anti scalding valve was getting stuck, and the pressure changes of opening more faucets, or maybe water hammer effect from opening and closing would make it work for awhile.
If you installed a new one at your new water heater it might be defective. If you kept an existing one it may be worn out or have minerals trapped in it - sometimes things like that never cause a problem until you turn the water off and it moves around.
Also check under the sink to see if it has an anti scalding valve. It might need replacing too.