TPS61046 wrong output voltage and high current consumption
When I test its operation supplying it with a laboratory power supply
set to 3.7V max 0.1A I get the consumption of 2.4V@0.097A, that is,
the TPS61046 is consuming -IMO- an excessive amount of current.

If your output voltage is meant to be 12 volts and feeding 3 parallel LEDs each with a current limiting resistor of 400 Ω then, each LED will take a current of approximately 10 volts ÷ 400 Ω = 25 mA. With three parallel circuits, that's a loading current of 75 mA.
So, that's an output power of 12 volts x 75 mA = 300 mW.
That's going to require an input power of about 333 mW (taking into account an efficiency of 90%).
So, if your input voltage is 2.4 volts, the current needed from that supply is going to have to be at least 139 mA. Hence, you have set your current limit too low in value for this circuit to start up properly.
Maybe you need to re-examine you current limit setting and be a bit braver.
Also, your L2 inductor; it doesn't look like you fitted the correct one as per your data sheet link. The DS implies a footprint size of 2 mm x 2.5 mm yet, in your picture it looks a little small.