Water – Gas water heater burner flame goes orange as I turn temperature dial up

It may be built into the design of the heater; kind of like most cars' cooling systems, the blower may be staying on to evacuate any remaining combustion gases and cool the heater element to preserve it. However, if it never shuts off, ever, there's probably a bad sensor or relay in the system that is keeping it running.

This manual for a State Select gas-fired water heater states "Due to the nature of the typical gas water heater, the water temperature in certain situations may vary up to 30°F higher or lower at the point of use such as, bathtubs, showers, sink, etc. This means that when the temperature adjustment dial is set at the mark approximating 120°F, the actual water temperature at any hot water tap could be as high as 150°F or as low as 90°F." (page 16).

Given your low temperature setting, it seems pretty likely that you are experiencing the expected behavior for this unit. You might consult a plumber to see if you could get a more consistent temperature by setting the thermostat higher and installing a mixing valve to regulate the temperature to your desired level. This might also give you an option to have hotter water available to certain locations (i.e., dishwasher) that don't present a risk to your kids.