

This question doesn’t really have an answer because the Internet, by itself, doesn’t have an amount of data at all. The Internet is a computer network; it transmits data, doesn’t store it. Computers connected to it do.
So you are going to need to define exactly what you mean, such as: all data accessible through the Web? Only data accessible to the public on the Web? Also data accessible through other services than the Web, such as emails on servers with no webmail interface?
Even then one problem with the question is that some data is stored more than once, for example this comment of mine will be federated to several fediverse instances, do you count it once per instance? Once per physical copy made during the operation of that instance (such as backups)? You can see that the question suffers from poor definition.
















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Some websites still have it, for example youtube.com and openstreetmap.org redirect to those URLs with www. in front of them at least for me.
Other comments already correctly explained that the original idea was that the third level domain would indicate what kind of server it is: www.example.com as opposed to irc.example.com, ftp.example.com, smtp.example.com, whatever. That convention existed before the WWW was invented; when it was, it was just yet another kind of service that existed on the Internet.
The WWW has by now developed into pretty much the default service people use the Internet for, so it’s usually no longer necessary to add www., although it’s still technically possible for www.example.com to point elsewhere than example.com, or even for one of them to work and the other not. Whether the version with www. redirects to the one without or the other way round, is something most people don’t even notice…
As for why we don’t say it, the reason is approximately the same: the WWW is now generally understood to be the default service of the Internet (many people don’t even know they are different things), so when you mention a domain name nowadays, it’s assumed by default that you are talking about what’s served on that domain on the web, not something else.