These are always tricky to diagnose over the internet.
Let's try this to see if the shower cartridge pressure balance is the problem.
Run hot water in the affected areas one at a time. Kitchen sink first and while running feel the hot outlet piping of the water heater. If the pipe gets hot then you know the tank lines are okay.
A cross over of hot to cold may make the cold supply to the tank get cold at first then gradually turn warm.
Take the face plate off of the affected shower. See if you can put your hand or a finger or even a meat thermometer on the cold pipe connecting to the tub/shower valve.
Open the sink faucet hot side and let it run while feling the cold pipe on the shower valve. See if it gets warm. If the toilet water is warm too, flush it and continue to feel the cold side of the shower valve. You may even hear or feel water flowing through it even though it is off.
Do the opposite for the hot side of the shower valve while running cold water from the sink faucet.
If you can access the pipes under the house you can also feel which pipes get hot or cold with use while somebody else opens faucets, communicating by phone during the process.
This works best with sink faucets that have hot only and cold only handles.
If you have single handle sink faucets, they could also create the same situation. Debris from the repair could be boogering up the cartridges.