Definitely looks like a conversion from steam, with a small DHW coil that red ~5 gallon buffer tank on the boiler bypass.
Scrap the beast it's probably oversized for the load anyway, and guzzling 1.5-2x as much fuel as newer-better stuff would. Go for something gas-fired & lower mass, maybe "high efficiency" condensing, maybe not, but DO make sure a careful heat load analysis is done, and that the boiler isn't oversized for the heat load or you'll pay for it in fuel every year.
Rather than an embedded tankless coil for the hot water, get an indirect-fired tank operated as a third zone with "priority" control. It'll put out way more hot water at much higher efficiency than a tankless coil embedded in the boiler (or the tiny coil in that red bucket you have there.) If one of your zones is much bigger than the other (like 3-4x as big), you might be better off using a "reverse indirect", buffer/heat exchanger from which the zones draw, with the boiler set up on it's own loop. Otherwise the boiler would short-cycle on the smaller zone, which will rob it's efficiency. A buffer in the middle sort of averages it all out the same way high-mass boilers do, but with much better insulation they have lower standby losses. A buffer with an internal heat exchanger for hot water is less expensive than a separate buffer + indirect tank.
Also, when setting up a new system with the full heat load analysis in place, set it up to run at the lowest temperature that delivers enough heat to the coldest room on the coldest day (or use responsive controls that sense outdoor temps and raise/lower the water temp as needed). Every 10F you lower the water temp in a hydronic system saves ~3% in fuel use. If it's set up for 180F, but could deliver the heat at 150F you're burning 10% more fuel than you need to. If it can deliver the heat at 140F or less, that's when a condensing boiler will really save a lot (25-35%), when combined with outdoor temperature sensing (a feature built into most condensing boilers.)