OK, that helps. They sent you the sheets for both the hub drive and the mid drive. Your mid drive motor spec is listed on the second sheet (48v G340, more commonly known as a BBS02b). The shift delay switch they install shuts the motor down (much like the brake switch would) when the shift cable moves. It's just for a second or less though! This switch should let you shift like you always have, but there is a timing issue you have to get used to. The derailleur moves like you are used to, which just starts the actual shift. The actual shift is not lightning fast. It occurs during what, maybe half of a crank revolution? So in practice, you initiate the shift, the switch does it's thing (that you may or may not notice), while you continue to turn the crank with no pressure. You'll "feel" when the shift is completed, and at that point you can start applying pressure on the pedals again.
I've been riding a long time too, previous to my mid drive e-bike, and where I got in trouble shifting the new mid drive was generally at low speeds (under 10 mph) and high loads, as in rounding a corner at low speed, only to be faced with starting a hill climb that I hadn't anticipated. During the time it takes to drop a gear or 2 for that climb, the bike will nearly stall (stop!), making it very difficult to recover because it's going so slow. In this situation, I would suggest that instead of dropping the 2-3 gears you didn't anticipate soon enough, bump the PAS level up a couple notches. From 1 to 3 for instance, or use the throttle so the bike doesn't stall. Use some of this motor's torque to build some momentum, and when your momentum recovers, THEN drop those 2 gears without crashing the chain on the gears.
Give yourself a chance to get used to it. It IS just a little different..... I'm at about 1500 miles on mine now, and the chain still has very little wear on it, indicating I didn't tear it up too bad while getting used to it. I don't notice the switch working at all, and shifting seems completely normal (almost brain dead).
Know too, that this is a "tuneable" controller in this motor. It's a giant rabbit hole though. If you want to invest in the time it takes to come up to speed on the tuning, it can be easily worth the trouble. -Al