Increasing prevalence of price discrimination
For current data, you could use a scraping program to collect data from firms' websites. This was the approach taken by a recent paper for airline pricing, so it would definitely work for your first example. In general, it should work for any market that has a significant online presence with universal price quoting. Retail sales should more or less satisfy that description. Grocery stores too nowadays, at least the big ones. See the paper cited for more info on its methods.

But, as your question pertains to the evolution over time, you'd need past data as well. Have a look at The Billion Prices Project at MIT and Harvard. http://www.thebillionpricesproject.com/datasets/

Williams, K. R. (2017). Dynamic Airline Pricing and Seat Availability (Cowles Foundation Discussion Papers No. 2103). Cowles Foundation for Research in Economics, Yale University. Retrieved from https://ideas.repec.org/p/cwl/cwldpp/2103.html