I have my own method to obtain quantitative data from other sites, it might not be exactly what you are looking for, but it might help.
Basically, my method relies on extracting data from the sites I want to learn more about (I use https://data-miner.io/) and track at the changes made over a specific period of time (e.g., navigation, layout, sections, content). This is, of course, works based on the assumption that they are continually releasing new improvements focused on areas of the site that aren't working well. Given this is true, whatever change they make that stays untouched, I assume has improved something for the best, after a while, the insights become very useful and interesting, but it might take a few months to gather enough data.
I've recently used this method while researching various second-hand online marketplaces. I wanted to measure how long it took users to sell their products on average, which products had the most views or likes and how those numbers evolved daily. This gave me a lot of insights into the issues users might find in the marketplace, the impact of promoted listings vs. free, the demand vs. offer discrepancy etc.