What you are experiencing sounds normal behavior for an automatic transmission w/over 100K miles on it. My 48 year old truck’s C4 transmission did that when it was new, and still does it, but that’s yester-years technology. Newer designs are smoother shifting.
The reason it happens is b/c it takes a lot of force from the transmission’s hydraulic system to shift the planetary gears into position for the shift. The hydraulic system consists of a pump, a bunch of tubes, and various valves (some mechanical, some electric solenoid) and associated actuators. Those all use seals, and the seals begin to leak a little with time and use. New transmission fluid of the proper spec fluid contains seal conditioning chemicals designed to keep the seals pliable and that makes them seal better. Have you ever seen an oil filter wrench, the type with the metal band that wraps around the filter? There’s something that looks like that inside your transmission too. The band is tightened around a drum (a sort of cylinder) by hydraulic force, and this causes the shift. Over time the band and drum surfaces can wear a little, which results in play between the band and the drum. Some transmissions — such as the Ford C4 – can be fairly easily adjusted to reduce the play in some of the bands. The 2nd gear band adjustment on the C4 just requires tightening a bolt as I recall. Not sure if something like that is possible w/your though. There are clutches inside the transmission involved with shifting too, but those usually aren’t adjustable. They have to be replaced when they wear out.