Private browsing helps prevent browser-based tracking, but doesn't help at all if both sides are playing together and have ways of correlating your identity.
I find this incredibly annoying, and also pretty spooky.
Instagram, not Snapchat, but yes. That's the main part of how they build "shadow profiles" of people without accounts, afaik.
They got me still.
So they know "John Smith" whose friends with "Joe User" on Facebook, has an email address for "Joe User" that is different than the one listed for "John Smith"'s account; now they have both. That's part of their business.
Personally, I own a domain. Every retailer, website, etc. I interact with gets their own email address. I have no doubt Facebook knows some of them, and can maybe even connect some of them to my profile -- but it's not certain.
P.S: I don't even use facebook myself.
However, I’ve received several LinkedIn and Facebook invites to these emails from businesses I interacted with - so I know LinkedIn and Facebook (at the very least) have — at least in the past — failed to make the connection between identities.
Also, I think FB recognizes residential IP addresses and associates activity from the same IP. I occasionally see Friend recommendations with ppl from ppl that I shared the same IP address with, but normally would not know.
One of Facebook's largest businesses is allowing companies to advertise against first-party data, ie lists of activities the customers upload. Crucially, these don't require a cookie sync; facebook matches against any of name, phone, zip9.
https://www.facebook.com/business/help/2082575038703844?id=2...
Naturally, there's not really a way to buy something without presenting this information to the retailer.
What can help OP is this: if in CA, go to the ecommerce company and submit a Do Not Sell request. If in EU, submit a deletion request. NB: for the latter, they will be able to retain information like shipping, etc. If in none of the above geos, hope the retailer is nice and gives the whole world the same rights.
Edit: You can also go into your FB ad 'privacy' settings and turn off some of the targeting stuff, for instance 'Ad based on data from partners'. You can also dig around there for a log of partners FB thinks you've 'interacted' with. Turning this stuff off gets rid of the spookiest ads and things like retirement facilities ads because you set your age to 103 when you created the account.
This is the problem, so many companies are harvesting our data now it's almost impossible to know how your personal data is being acquired anymore.
That being said, another thing to look out for is sites and apps running Facebook's integration crap. If the e-commerce site in question is running Facebook's code on the site, FB could easily correlate the data (IP address, browser fingerprint, etc.) and connect it back to you even if you are using Private Browsing.