Is draining a Li-Ion to 2.5v harmful to the battery?

Yes, lithium batteries undergo unwanted chemical reactions when discharged below 3V, causing their internal resistance to be permanently and significantly raised. Their capacity will suffer as well, meaning that they won't accept the same amount of charge anymore. When such an overdischarged cell is "brought back to life", it will likely become chemically unstable, creating a risk of a short circuit developing inside the cell.

Even worse, assuming that you measured 2.5V at no load, your batteries have dropped even lower when they were being discharged and have subsequently rebounded to 2.5 V after the load was removed.

Li-ion cells have a maximum voltage of 4.2 V or less, I am not sure where you got the 4.7 V figure from but it's a recipe for fireworks. OP has since edited the question, to a still incorrect 3.7 V. 3.7 V is the nominal voltage (average voltage during a complete constant current discharge), while 4.2 V is the maximum voltage. These figures will vary slightly from cell to cell.

I would completely discharge the cells and get rid of them, 2Ah 18650s are cheap and not worth the risk of them blowing up.

Yes, depleting a rechargeable battery under certain voltage level is harmful to the battery. The discharge voltage level depends on the battery chemistry.

The minimum discharge voltage varies between various sites, datasheets, etc. but 3.0V - 2.7V is an empirical value. If discharged under this voltage the battery may be permanently damaged.

To get the precise value of min discharge voltage, consult the datasheet of your battery.

And that when it goes below 3V a microchip disconnects the battery to protect it from discharging too far.

That's true, for batteries that have built in protection circuits. Not all batteries do. Most Li-Ion batteries are raw cells that do not. The ones that do will be slightly longer than the raw cells.

There is also circuits for multiple cells, and in various variations of externally visible or not. You can purchase the cells with the protection built in or purchase the circuits by themselves. Not just for 18650, all form factors of Lithium cells can have them.

You obviously have a non-protected cell, and because you didn't add a low voltage lockout, drained it beyond the safe limits.