A system pressure of 12psi is fine for any 1-2 story house. In taller houses it make take higher pressures to keep sufficient pressure on the system on the upper floors.
If the system was brought up to 12psi when the average water temp in the system was >130F it might be as low as 10psi cold, but not any lower.
To determine the minimum size for the expansion tank the total system volume has to be added up, including the volume in the boiler + radiators + plumbing. Then the difference in water volume has to be calculated between the room temp and the peak operating temperature of the system. The volume of 180F water is larger than 140F water, which is quite a bit bigger than 70F water, when the system is off. The expansion tank needs to be sized to handle the difference in volume between room-temp and the average water temp at the highest operating temp. If the replacement tank was the same size as the failed one it could still be too small- they should have done the math on the system volume and the difference in volume that occurs when the temp is raised by at least 80F, 100F would be better, to have some margin. The AWT on the system is probably something like 150F when the boiler out put is 160F, and the difference between a ~70F (when the system is cold) and a ~150F AWT is about 80F.
The fact that you have big radiators rather than fin-tube, and from the photo it looks like at least some of the distribution plumbing is done in 2" or 2.5" piping, your volumes are going to be MUCH bigger than "typical" systems, and simple-minded sizing charts based on radiation type and boiler sizing just don't apply. It's conceivable that the installer just took a WAG at it or used a manufacturers chart and got it wrong. Monitor the pressure and temp as the boiler is heating up. If there is a clear temperature at which the pressure crosses 15psi. If that temp is under 150F it's an indication that the tank is undersized or not properly charged. If the system is set to 12psi when cold or tepid (long after the burner has last fired) ideally it wouldn't rise much above 15psi with a right-sized expansion tank, but NOTHTING LIKE 22psi (a 10psi rise). If it's been "normally" running at 25-26psi, it's anything but normal, if the cool or tepid pressure was set to 12psi. A 2-4 psi rise would be typical, and even a 5-6psi rise might be OK (but not ideal). With a 6psi+ rise at a high-limit of 160F, if you adjusted the high limit up to 200F (which is a perfectly legitimate thing to do) you'd be almost guaranteed to blow the PRV.
Since you're getting a 10psi+ rise on the system you are likely hitting the designed acceptance limits of the expansion tank, beyond which the pressure then rise rapidly with temperature (which is when the PRV opens up to prevent a more destructive pressure release somewhere else on the system.) PRVs are not high-precision instruments, but those used on most hydronic systems are designed to open up at 30psi, which is the top operating pressure range of many hydronic system components, (including many cast iron boilers). There's usually a metal tag indicating it's design pressure, and I'm assuming yours reads "30psi"(?). If it's spittin' a coupla cups, it really IS hitting that pressure (or close to it), independently of what the 57 year old pressure gauge on the boiler says. If the PRV is also that old, it could be way out of calibration and opening up at lower pressures, but I'd still trust the PRV more than the pressure gauge. And if you're running 12psi tepid/15psi hot like it SHOULD, it doesn't really matter if it's kicking open at 25psi instead of 30psi.
If you do your own system volume arithmetic you could
play around with this sizing tool as a sanity check on the size of the tank that was installed. Or you can use
the simplified instructions found here.
In the meantime, note the temp at which the pressure takes off, and dial back the high-limit on the boiler's controls so that it stays below that temperature. If that temp is 150F you may be fine forever running the system at that temp, but if it's 140F it's a problem, since the return-water temp would likely be cool enough to cause destructive condensation in the flue and on the boiler's heat exchangers, and you may not have sufficient radiation to deliver enough heat at 5AM on the coldest day of the year at that temp. (If you DO have that much radiator, that's a very good sign for being able to hit mid-90s for system efficiency with a modulating condensing boiler under outdoor-reset control once the reset curves are adjusted.)
The nameplate on the boiler probably has both input and output BTU numbers on it. If it's still readable, divide the output number by the input number- that's the absolute steady-state efficiency of the boiler when it was new. (Eg: if output=61,000 BTU/hour, and input =80,000BTU/hr the steady state efficiency is 61,000/80,000= 0.76, or 76% efficiency. A mid-50s boiler may be as high as 80%, but many were running in the mid-70s on day-1, by design. Standing pilot ignitions and lack of automatic flue dampers would typically bring the as-used average down to about 70% or less. Yours clearly doesn't have the damper, which would typically be mounted just above the dilution air hood (the black piece on your stack) where it enters the exhaust venting. It was a popular efficiency retrofit to add the automatic flue dampers in the late 1970s, and they became standard equipment new boilers to be able to pass minimum AFUE requirements that became code around that time.
It's not worth adding efficiency enhancements to the boiler at this point- it's time to scrap it, say "good-bye" to your good-buddy and get something newer/better, and right-sized for your actual heat load. The heat load can can be estimated with reasonable accuracy from the name-plate efficiency of the old boiler and a mid-winter fuel bill with the meter reading dates, to measure fuel use against heating degree-day data. But a new boiler won't change the expansion tank requirements by much. (And it would be slightly smaller, not larger- the old boiler probably has something like 5 gallons in it, and a mod-con might have 1 or 2, but I'm guessing your system has several 10s of gallons in it. An oversized expansion tank works just fine.) If you replaced it with cast iron boiler you'd be limited to ~83% efficiency if you wanted to use the same flue, and even then it might require a reducing liner if the flue is too big for the right-sized cast iron boiler. Higher efficiency cast iron exists, but it's all forced-draft and would likely need more expensive venting materials than a mod-con, (narrowing the installed cost difference) and the very high end is ~87-88% AFUE.