No, you are not harming yourself. Your body is not going to start digesting itself for lack of fuel in 3 hours. Nor will it in four hours.
At 7am, your body still has energy from the food you ate yesterday, and that’s how you are getting your exercise done. Then you are putting yourself into a state (hopefully) where it needs to burn some fat to fuel you and to start the muscle repairs that the weights make necessary.
It knows how to do all of this on its own. The people that need the energy replacement are professional athletes, body builders, people trying to actively put on bulk, etc. Those people who are training 10 times harder than a regular person and trying to get bigger, faster, stronger, and already at very low fat stores, those people need to replace the energy right then.
That has translated into people believing that they need 32 ounces of gatorade after a walk around the block, because that thinking sells Gatorade.
Those 3-4 hours are not going to make you die. Nor is your body going to digest its own heart or any other muscle.