After 23 years of steady water flow when using toilets and all taps in our house, we noticed that in the last few weeks, whether it is in using the shower, or the toilet refilling, the water ebbs, then flows harder, then ebbs again, continuously. At first it was slight. Now it has become more pronounced. We are on a well, the pump was replaced a year ago, and our area is above its rainfall quota at this time. Does it sound like a problem with the pressure tank?
Yes, it does sound like a pressure tank problem. Without a properly functioning pressure tank, the well pump has to try and maintain pressure with fluid alone. That's what you're seeing at the faucet--the cycling of the well pump as pressure very quickly jumps and drops.
The problem could be a tired bladder or a leaky seal elsewhere. Try re-pressurizing the tank according to the manufacturer and see if it holds, and check for leaks at the fittings.