Why is my circuit's current far lower than expected with 2.6v / 220Ohm / and LED?

The diode has a forward volt drop of 1.775 volt hence the current that this circuit drives might be only (2.6 - 1.775)/220 = 3.75 mA.

You don't have the full 2.6 volts across the resistor hence 2.6/220 is meaningless.

If you are dropping 1.775V across the LED, you only have 0.825V across the resistor and that equates to 3.75mA. I = (0.825/220) using Ohm's law, so what you are measuring is right.