Q: A slight lunge in very beginning of 1st gear

At a stop, I accelerate like you would normally, and I feel a very small kind of lunge right in the beginning of 1st gear. It's pretty subtle, but it's there. I do not feel it at all if I hit the gas harder from a stop, not floor it, but quicker acceleration. Otherwise, from then on all the shifting is very smooth. Vehicle had the TCM module replaced in 2013 after van was stuck in limp mode, fixed the issue. Not sure if this new issue is transmission related though?

Here's a video I took of it happening. It may look as if it's just shifting from 1st to second, but it happens so immediately in the beginning of first gear and the vehicle has hardly even started to move when it happens: https://youtu.be/79PtXpNZPcU

Also, here are some photos of some signs of leaking fluids: Under trans.: https://ibb.co/fdCUBG https://ibb.co/m3ELJw https://ibb.co/bVwBQb

Above trans.: https://ibb.co/hVGZdw https://ibb.co/gkQu

Any idea what this slight hiccup in the beginning of 1st gear might be? Thanks

My car has 118000 miles.
My car has an automatic transmission.