1. “HDR” is often referring to a tone mapping to convert the 10-14 bits of dynamic range in a camera’s raw file into the 8bits that fit into a jpeg (and often the screen).
2. HDR also refers to actually showing more than those 8bits of information. Saving more than 8bits in the image and having a screen that can show more than 8 bits of color.
#1 is real easy to make look unnatural, and most phones go over the top with it. #2 is a straightforward improvement and basically always makes the photo better.
FWIW, I've felt over the years that if you have to get used to it, it probably wasn't that good to begin with: so so many things that are totally different I've upgraded to and thought "omg this is amazing! how did I ever live before?" and, if I have to go back, it takes a long time to get used to the bad thing again.
The one example I have off the top of my head: higher resolution monitors. I was totally happy with my lower resolution monitors; but, the second I tried a higher resolution monitor, it ruined me for lower resolution monitors. I can totally get used to it again, but it takes a long time, and I really don't want to; upgrading, though, is instantaneously better.