Firefox’s free VPN will offer 50 gigabytes of monthly data, which is pretty generous for a browser-based VPN. A Mozilla account is required to make use of it, which isn’t a hardship (they’re free), but is a point of friction some may wish to know upfront.
If you have to install any closed-source software to use the VPN, the answer is oh hell yes, they can install a root cert. If they are clever they can remove it when you disconnect, so it will not be noticed by most people.
Even if they require no proprietary install, by definition the VPN knows every IP address you connect to. Even if you use DoH. Even if you use Quad9 DNS. The VPN knows you visited midwestsluts.com
If you want privacy, either spin up your own selfhost OpenVPN, or use the Tor nodes myself and other volunteers pay for, to make free for you to use.
Tor node operators can’t tell what site you are visiting (if they run an exit node they can see the site – but don’t know your IP; if they run a Guard/proxy node they can see your IP, but can’t tell anything about what sites you visit or what data you get)
Joke’s on them, because half the web is behind CloudFlare now.
What if the gov has access to both tor nodes, cloudfare infrastructure and mozilla servers?