I have low hot water pressure
I have a similar yet different issue - mine is low hot water pressure at the Kitchen and high hot water pressure at the Master Shower -
Installed a Recirculating Pump on the Water heaters - at the same times replaced both valves (have an inbound (cold) and an outbound (hot) valve) on the water heater (gas), both valves had rust buildup internally and the nipple going into the hot valve from the water heater was nearly rusted through. Also drained the water heater. Installed the recirculaing valve under the kitchen sink. Filled the hot water heater and "thought" I had all the air purged, not only from the tank, but from the water lines. Water flowing normally at the Kitchen Sink, turned on the recirculating pump. Water pressure on both sides (hot & cold) suffered a 25% to 50% decrease. Went to take a shower later in the day, turn on the shower, gigantic release of air and then incredible pressure probably 75% higher than in the past.
The only things I can think of are: Kitchen Sink - shut off valves below sink obstructed.
Shower - pressure reducer in shower head blown out by the air pressure.
Live in an area with hard water and I have a water softener on the main inbound water line to the house.