If the air pressure reads 13 when the system pressure is north of 15 it means there is not much expansion space for the water as the temperature changes. Pump it up to 20psi- the system pressure will rise with it. Then (without getting scalded) bleed the system down to 13-15 psi, and re-measure the air pressure. It will probably have dropped. Repeat a few times until pumping the tank to 20 psi doesn't change the system pressure, then back off the air pressure to the system pressure + 1 psi. Then you'll know the full volume of the tank is available for water expansion.
Even at the highest blower speed the 3- ton
36HBXB-HW only delivers ~60,000 BTU/hr at an entering water temp (EWT) of 180F. With the 1.05 gph nozzle it was probably in the burner the
PV83 is giving it about twice that (see Table 1.B in the manual), so during long calls for heat on the air handler zone it should be hitting the high limit, cycling on & off. (That's not a great way to run the boiler from an efficiency point of view, but that's the behavior you should expect.) Burner techs usually leave a tag with information about combustion efficiency, nozzle size (or part number) when the tune up an oil-burner- see if you can verify the nozzle.
Depending on what other radiation (type & amount) there is on the other zone it may be worth down-firing the boiler with a smaller nozzle to limit the number of burn cycles bumping up net "as-used" efficiency a bit. It looks like a 0.75gph nozzle was standard for the "WM" version of the _V83.(Table 1.B in the manual.)
Unless your house is enormous and uninsulated it probably doesn't need anywhere near 3 tons of cooling or 120KBTU/hr of boiler. A typical reasonably tight reasonably insulated 2000' rancher in CT would have a design cooling load between 1-1.5 tons, and a design heat load under 40K (for the whole house, not just one zone). It's common to see big (even ridiculous) oversize factors in houses, but it's not great for either efficiency or comfort (often the opposite.) It's not cost effective to swap out a fully functioning HVAC system, but if you're ever in the position of needing to replace piece it's worth taking the time to figure out how to right-size it. At the current cost of #2 oil and electricity in CT a right-sized modulating ducted cold-climate mini-split heat pump would be both more comfortable and have a lower operating cost.