Pre-COVID I travelled a lot for work and so I drove lots of rental cars. Nothing fancy, generic Avis or Hertz sedans. But it always cracked me up how I'd get in the car, pull out and step on the brake the first time and come to a screeching halt because they are way more sensitive than the ones on my car and I pushed the pedal too hard for that car. You're dead on, blind spots are different, handling is different, sometimes it doesn't matter much but sometimes it's a big difference and it really does.
A few years back, I rented what was classified as a “full-size” sedan. I hadn’t ordered it, but they were out of whatever class I had ordered, so they upgraded me. The thing had massive front fenders, at least compared to what I’m used to, and damned if I didn’t nick the right front fender on a concrete barrier in a parking garage. Ugh. In my own car(s), the turn would have cleared that barrier without incident. But I wasn’t in my own car(s), and it didn’t. Thank God for insurance. LOL.
When I get into a car that is not my own, any car, I take extra time to adjust everything...seats, mirrors, I familiarize myself with the controls, the emergency brakes, wipers and as you said, when I put it into gear and also apply brakes very carefully. I too have had that sudden jerk to a stop when applying brakes you are unfamiliar with.
Before I put it in gear, I check out the visibility and all the blind spots.
But then again, I am one of those people who always backs into a spot or pulls through, because I feel that when you are driving, warmed up and oriented, driving in reverse to back in is safer and easier than coming out cold to your car, being distracted, and backing into a busy area.
Always better to nose out and go when you aren’t “warmed up” and oriented, rather than backing out and going.