Makes no difference. All that dns does is convert a name to a ip address. The pc then only uses the IP address. In many cases the pc also has a cache someplace for that information that it keeps for a very short period of time so it doesn't constantly ask the DNS server. This is at the OS level it is not the browser.
The only complexity is many browser now have the ability to override the DNS. This was very useful for the year or more before microsoft added encrypted DNS to the OS. The problem now is you have to make sure that the browser is not over riding since you can set the browser to use a non encrypted dns server even when the OS is set to use one. Pretty much more places to make a big mess of stuff if you are not careful what you change.
Browser history is the names of the sites it does not keep of what IP it resolves to. This again is because the IP addresses can change a lot. Do nslookup
www.google.com
You will see a list of IP and the order can change everytime you do the command. It also likley changes if you use different DNS servers.
A so called web "server" is no longer just in one location or one physical machine.