Winter peas are a great cover crop and you haven’t done anything wrong so don’t fret! You have three choices which are hoeing, tilling, and pulling. Why pull them if the point is to increase biomass as you said? I don’t think that’s necessarily the point of a cover crop. The point is to keep the soil alive and active over the winter. Otherwise the bugs and bacteria die and the soil gets compacted.

Whatever you choose, you should add 1/4” of compost to the soil anyway. There’s your biomass.

So don’t worry about pulling and removing, put them in your compost bin and make the next round of compost to add to the soil. When you pull, you will still leave behind many fine roots with those nitrogen fixing bits on them although (according to author Steve Solomon ) the impact of that nitrogen is negligible and over exaggerated. You should still add compost and fertilizer to a vegetable bed.

If you till them in, their nitrogen content will make them break down rapidly in the soil and yes increase biomass and humus and also leave the soil more aerated. Won’t take long at all before you sow veggies again

Hoeing would be my favorite choice if the area is smal enough that you can reasonably do that. Aim to chop the plants just below the surface of the soil while leaving all the roots in place. Use a sharp hoe. This way you leave the soil structure in excellent shape and as the roots rot they make channels for air and water down into the ground. Remove the plants and compost them, add a bit of rotted compost and some fertilizer. Hoe or rake them gently into the top inch of soil. You can even just leave them on the soil surface and let the bugs do the work for you. Keep using winter peas it’s a good choice.