I don't know that I've necessarily gotten more sensitive to caffeine with age, but since I gave it up completely (more on that in a second), I've noticed that even a little bit will have a dramatic physical and psychological effect.

Some background: I gave up caffeine back in 2015 as an experiment. I asked my gyno why I was having severe breast pain at frequent random times instead of just at certain points in my cycle, and she explained that this could be related to ovarian issues (which were ruled out with a blood test) and caffeine usage. I decided to cut out caffeine for a month to see if it made a difference in the breast discomfort. Boy, did it! I almost never have breast pain any more. Sorry if that's TMI; just thought it was interesting to note.

The other significant change I noticed was a dramatic reduction in the physical symptoms of my anxiety (I have General Anxiety Disorder). I used to get heart palpatations over the most insignificant things. That stopped after I gave up caffeine. My resting blood pressure went down to the point that it's almost too low sometimes! Overall I felt much more calm and relaxed. I started sleeping better. That's why my temporary avoidance of caffeine has turned into a permanent one.

It sounds like the physical changes you describe (the palpatations going away) are very similar to my experiences. That suggests to me that caffeine can indeed have more of a physical effect than we realize. I used to think that I had a high tolerance because I could consume a lot of it without feeling any more awake than I did before. Apparently it was just stimulating me in other ways besides wakefulness.

As far as an increase in sensitivity? Hard to tell. But now that I've given it up, I have to be very careful. I take Excedrin for migraines, for instance. It's the only caffeine I consume except on the rare occasion when I give in and drink regular tea instead of herbal tea (and whatever minute amount is in decaf coffee). I learned the hard way not to take Excedrin before bed - not only was I awake all night, I had a full blown anxiety attack! Not good. So anyway, I'm not sure how sensitive I was before but I'm definitely highly sensitive now that I've given it up.

Hope that helps answer your questions.