Does drinking coffee immediately after lunch or dinner impact health? Does drinking coffee immediately after breakfast or lunch or dinner impact health?
I think this is a rather broad question to answer. Are you looking for overall health effects of coffee or specifically for effects on digestion after eating?

In the former case, recent research has delivered very strong evidence that drinking a moderate amount of coffee (about 3 cups a day) has strong positive health benefits, reducing premature mortality quite dramatically. Among others coffee likely has positive effects on cardiovascular diseases, can be preventative to some types of cancer and alzheimer diseases and has positive effects on diabetes. See for example here, here and here.

The latter case is less conclusive I think. There have been studies showing that coffee (the chlorogenic acid in it) reduces glucose intake from digestion. While a decrease in nutrient intake seems like a bad thing at first glance, it may be beneficial for patients of diabetes, because it regulates glucose intake after meals and may help in preventing spikes/drops in insulin levels. I guess for someone struggling to get enough nutrients (due to other digestive diseases for example) excessive coffee consumption could have adverse effects. For healthy people moderate amounts most likely don't have negative effects (see the linked studies). There's also some evidence that coffee has beneficial effects on your microbial composition in your intestines (see here)

There's some other less severe potential issues that might arise, like an increase in reflux symptoms, due to excessive production of stomach acid (however dark roasts of coffee might even have acid reducing effects).

So overall I'd argue that the potential health benefits by far outweigh negative effects, except maybe in some cases of pre-existing conditions such as diseases of stomach and/or intestines.

References:


Gunter M. et al. Coffee Drinking and Mortality in 10 European Countries: A Multinational Cohort Study. Ann Intern Med. 2017;167:236–247. doi: 10.7326/M16-2945
Jaquet M. et al. Impact of coffee consumption on the gut microbiota: A human volunteer study, In International Journal of Food Microbiology 2009; 130.2: 117-121, https://doi.org/10.1016/j.ijfoodmicro.2009.01.011.
Poole R. et al. Coffee consumption and health: umbrella review of meta-analyses of multiple health outcomes. BMJ 2017. doi: 10.1136/bmj.j5024
Song-Yi Park et al. Association of Coffee Consumption With Total and Cause-Specific Mortality Among Nonwhite Populations. Ann Intern Med. 2017;167:228–235. doi: 10.7326/M16-2472