Why would I have hot water at one faucet but not the others?
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.