The "T & P" stands for "temperature & pressure", and are required on hot water heaters. Hydronic boilers typically have a pressure relief valve or "PRV", that is temperature-insensitive, only opens up when the pressure exceeds it's threshold.
The PRVs shipped with most boilers are set to open up at 30psi. These are not precision instruments, but it'll usually be within a pound or two of that.
That looks like a Burhham P205 or P206? On a '90s vintage P- series there is a pressure & temperature gauge inside the front panel that you remove to gain access to the burners & controls. For a 2 story house with the boiler in the basement the system should be running about 12psi unless you have an unusually tall house. The expansion tank needs to be pre-charged with air to the same pressure that you are running the system. If the the pressure is over 12psi when the system is cold or lukewarm the system pressure is too high.
On a converted steam system there is a lot of water volume, which means the amount of expansion volume difference from when it's hot to when it's cold is substantially higher than on a low water volume system such as baseboards. (The radiator volumes and pipe diameters are considerably bigger.) This means that the expansion tanks will need to be bigger too, and it's possible that yours is sized at the margins. If the system is about 12psi when cold, the pressure will rise a bit as the water warms up and expands, but most of the expansion should be tanken up by the expansion tanke. When fully hot and running it should never go over 25psi unless the expansion tank is undersized or incorrectly charged, or the system pressure was initially set too high.
Often when a PRV opens up once it catches some grit from the heating system water and doesen't fully seat, which could cause it to continuously dribble, but if the system hits the ~30psi even every-other burn cycle you'll be getting constant re-wetting.
Auto-fill valves can fail and over-pressurize the system too, which could be another thing to check out.
A Burhham P-series is nearing end of useful service life at age 23. The heat exchanger plates are usually sufficiently corroded (on both the fire side & water side)at that age to affect combustion efficiency. On it's very best day it's steady-state efficiency was about 80%, and by age 23 it's not unusual to be running at 75% or less. Even though the thing may continue to run another 20 years with occasional repairs, it's not necessarily the "right" thing to do. It's time to at least start thinking about the replacement system, unless you're planning to sell in the next few years. For a typical 2000' house in IL built in the 1920s a P205 is WAY oversized for the actual heat loads, and a P206 is even more so.
With a ZIP code (for weather data) if you can track fuel use against the base-65 heating degree-days between meter reading dates at a nearby weatherstation on
degreedays.net it's possible to use the boiler itself as the measuring instrument (however crude) for determining the true heat load at any arbitrary temperature. If you're covered for the 99th percentile temperature bin, that's a very reasonable outside design temperature. Even though it gets colder than that 1% of the time, you're usually still in bed when it does, and you don't really lose much ground temperature-wise indoors until it's been way below the
99% outside design temp for many hours.
I suspect without an insulated foundation but with storm windows & some attic & wall insulation your actual heat load is between 40-50,000 BTU/hr, but in a tightened up better insulated 1920s house with foundation insulation it could be 30K. The P205 puts out 100,000 BTU/hr even when it has degraded to 75% steady state efficiency, and by being 2-3x oversized it's as-used AFUE is nowhere near it's nameplate number. Even the P204 delivers over 70K, even when it's old & decrepit. If you "right size" the replacement boiler it'll hit it's efficiency numbers, deliver longer more efficient burns, which will end up being more comfortable in the end.
Unless the boiler itself is leaking between the heat exchanger plates the replacement plan doesn't have to happen right away. Replacing a PRV is a sub-$50 repair as a DIY, an expansion tank is also in that order of magnitude. But if you have at least the sizing part nailed down in advance, you can then end up optimizing the system down the road when you pull the trigger on a replacement. Most heating & plumbing contractors will be inclined to just replace it with something of similar output, but 9 times out of 10 that's only making their life easy, since they know it'll keep the place warm, but it's not doing YOU any cost, comfort, or efficiency favors.
If you want to run a fuel-use based heat load calc I can explain in more detail how that works. (Or you can probably find threads on this site where I've explained it before.)