Yes, this is due to the various sorts of data stored by the site as you navigate to it or on it. This can be illustrated on sites where changes are intended to happen, there is often a prompt after you've made the change to close your current tab and reopen the site on a new tab. (This is not common on public websites, but it is common on business and enterprise tool web portals where you may be changing things like the certificates or other connection-related site functions).
It is usually far simpler to close the tab, open a new one (even in the same browser window), and navigate back to the site than it is to clear cache and then attempt to reload, and so that is the suggested action.
The reason this behavior is consistent across different OSes and browsers is that the browsers and sites behave similarly regardless of the OS. You'll observe very similar behavior in other Chromium-based browsers, but also in entirely different browsers such as Safari or Firefox.
More specifically, the thing that is most likely breaking when you connect a VPN is where the browser expects to find the website on the internet. It's like you got a map with directions from London, England to Seville, Spain and began your journey but then you are unexpectedly transported through a wormhole to Munich, Germany. Your map is no longer helpful, and the directions on it will, at best, not get you to Seville.
Changing the nature of the connection the way VPNs do, or other sorts of changes are uncommon events. The things that make browsing the modern internet easy and convenient and local-application-like require the connection to remain the same throughout the session, and changing the session's underlying connection significantly results in breaking the connection.
