Yes, please tell what sites don’t load, and confirm that the sites work from a different computer before concluding that it’s your Purism device and not something else.
If it turns out that none of your devices can connect to these sites, I’d start questioning what country you’re in (censorship) or if there’s a firewall / routing device upstream in your network that could be the culprit.
If it really is the PureOS device though - strange. I’d ensure your network adapter is running normally, then check your Firewall and HOSTS file to ensure those don’t have any rules in place for those domains either.
After that I’d start wondering if the sites in question block browsers that identify as using Linux in their User-Agent for some reason - the remedy would be to spoof it of course, but I’d wonder why anyone would do that.
If it’s none of the above then it must be something technical in PureBrowser that I just don’t know because I’ve never used it yet.
But, by the first sounds of it - the connection works on a VPN. That makes it sound like your country is blocking the website or a device upstream in your network is blocking those websites and your VPN is allowing you to tunnel past it. You’re not attempting to connect to these sites at your workplace are you? Did they work before?
But then you say it works after disconnecting the VPN as well. My assumptions are either that the VPN didn’t actually disconnect when you disconnected it (check your IP please) or that there’s something wonky with the network adapter. Many VPNs mess with the adapter setting and install protocols in order to function. This could’ve possibly messed something up. I wouldn’t be able to tell without sitting down at your computer and having a look-see though.
That’s about all I can come up with off the bat. Mind you these are all ideas I’m coming up with as a Windows user, so take them for what you will, I’m not a Linux user yet so for all I know it could be something in Linux that I just didn’t know exists. This is all just advice that I’d be giving to someone who’s having the problem on Windows.