The major reason for the extreme quietness is the absence of any explosions. Petrol and diesel engines explode the fuel thousands of times per minute. Silencers are essential.
In our small river/lake/canal Stirling boats we burn propane gas to heat the engine. This heat is the source of the power. The noise generated is the same as a kitchen gas hob. Thereafter, the only other source of noise is metal sliding against metal. A piston slides in a cylinder and the prop shaft turns in a ball race bearing. So, just as a bicycle has sliding and rotating parts, it’s much the same for a Stirling engine. If a bicycle is noisy, it is a sign that something has come out of adjustment. It’s the same for a Stirling.
Electric boats can make a “whine” noise at high revs. Perhaps a Stirling can be even quieter than an electric boat.
You and I talk to each other at a decibel level between 60 and 70 decibels. A while back, I measured a small Stirling stove fan at 34 decibels. This was late at night when there was no wind outside. Nearby Heathrow was inactive and I had to turn off the fridge and freezer. Their compressors disturbed the readings.
When out on the river in a Stirling boat we have measured levels of 50 decibels. But that included background noise from wind in the trees, other boats, the nearby M4 motorway etc.
The Stirling boat is VERY quiet – ask the captain of the USS Ronald Reagan.