Eating more fibre will slightly increase your metabolic rate, as it takes energy to move that fibre through your body and expel it (known as "Thermic Effect of Food/Feeding" or "TEF"), but this increase will be small and insufficient to significantly affect weight loss or gain. So no, it should not be possible that your calories are getting "thrown" away because of your high fibre diet.
Concerning the other things you mention in the context of your question:
I'm using huel powder to meet 1600kcals (so about 4 shakes per day);
the rest comes from real food.
Why? That's both a questionably high proportion of your total nutrition coming from a single food product and (assuming you're eating the remaining 1400kcal over three separate meals for a total of seven meals per day) an extremely high meal frequency.
I've noticed that I'm having to poop about 5-6 times a day, and it's
almost always after I've consumed a huel drink.
If you're taking 4 shakes per day, then pretty much every moment of your day is shortly after you've consumed a Huel drink. In any case, that's a lot, and could be result of all the fibre you're consuming, or could be a reaction to the xanthan gum in the shakes. Consult a dietician if it concerns you.