No hot water pressure
If you turn on the hot water and get a very small flow...
And can turn on the drain valve on the new hot water heater and get a really good flow... (place bucket under it of course.)
Then the problem probably is that an old disintegrating water heater sent particles through the water lines and these particles have clogged your hot water valves and faucets.
Try disconnecting a sink connection on the hot water side. Turn the hot water valve off under the sink. Disconnect the flexible tube which goes from the valve to the faucet. Place the tube into a bucket. Turn on the valve. See if you get good flow.
If you do, then place the bucket under the still disconnected faucet. Turn on the hot and cold at the same time. Then place your hand over the spout. This causes cold water to go in one side and backwards out the hot side and into the bucket below.
This is called "back flushing". It will cause those particles to clear out of the hot side of the faucet.
Then reassemble the faucet and the hot should now work as good as the cold.
If that works, then back flush all the other faucets.
Note: If you do not get good flow from the valve in the wall, then the valve will need to be removed. Best that be done by a plumber if you are not experienced at doing this. Trying to remove those can break copper or plastic connections inside the wall if you are not careful!