The expansion tank (if intact) has a bladder or diaphragm keeping a bubble of air (which acts like a spring) separate from the system water (so the air does not dissolve into it and end up elsewhere, needing to be bled out and rusting iron/steel parts.)
The reducing valve (what I call an autofill valve) adds water to the boiler loop when boiler pressure falls below its setpoint. It does not remove water when its setpoint is exceeded - it only puts water in. For a typical 3 story building, pressure should be 18-25 PSI (1 PSI = 2.3 feet of head of water, roughly. So 18 PSI should vent up to 41 feet above. If your gauge is accurate, you're closer to 53 feet up at 23 PSI. 25 psi will push to 57.5 feet.)
Say your valve is set at 20 PSI, and the boiler is cold, and dropped to 18 PSI. The valve adds water until it's 20 PSI. Now the boiler fires up and becomes hot, and the pressure rises, because water expands as it heats (unless you are very close to freezing, where water is "interesting".) The bubble of air in the expansion tank compresses, so rather than the boiler and pipes quickly rising above 30 PSI and engaging the overpressure release valve, the air in compressed as the water expands and the pressure rises to some value less than 30, if the system is designed and sized correctly. Your boiler runs for a while, and then shuts down and starts to cool - the air in the expansion tank expands as the water in the boiler and pipes cools & shrinks, and if there are no leaks, the system ends up back at 20 PSI (at the boiler - less, the higher you are in the building) and no new water needs to be added.
The "Pre-charge" pressure on the expansion tank is typically just a little bit less than you expect the lowest acceptable boiler pressure to be, so that there's a little bit of water in it at lowest pressure, but room for more as the system heats and pressure rises. If the "Pre-charge" pressure is too high, no water is stored at lower pressures, and the system pressure will drop below fill pressure when the tank is fully empty but system pressure continues to fall as it cools. If the "Pre-charge" pressure is too low, lots of water is stored at low pressures, leaving less room for adding water and compressing air at higher pressures, effectively reducing the size of the tank, and possibly leading to operation of the relief valve as pressure rises too high when heating and expanding system water.