Does Google Chrome store browsing history on their servers? I think, if for example I use private browsing, Chrome can still log my activity.
If you're logged into chrome, and not using incognito, then sure.
If you're not logged in to chrome, they store a list of all the sites you've visited through their tracking cookies.
Assuming you're using incognito, there are lots of ways people track you. Here are a few.
If you're using private browsing, there is not local history, and there is no tracking cookies (unless you don't close the private browser, and there is a tracking cookie that maps all the sites you visit while using the private browser. So, if you login with gmail, then visit p..nhub, then google probably mapped you to that url and then yeah, you're in their records.
If you're using your ISP's DNS, then your ISP can see all of the host names you resolve. They also know your name, address, and credit card number. So if you visit p..nhub from your ISP, they have a record that you went there. They don't know anything beyond that if the sites you visit are HTTPS, but if they are HTTP, then they can see the pages you visit too.