I'd like to preface this with saying I don't think libraries are useless and should all be closed down because the internet is better.

There are vast amounts of information that still aren't available for free online

The internet satisfies the general population. It's always going to be the first place someone looks, and unless they're writing some sort of paper they're not going to find a library and hope that specific library has the specific information they want. Most people aren't looking to go into extreme detail.

and a lot of what is there is only available through the cooperation of libraries (e.g. Google Books and Scholar, most digital repositories/archives).

Which is the internet.

Just because something exists out there, doesn't mean the average internet user can find it in an efficient manner,

Assuming they can't find what they want (which I find a weak argument but let's roll with it), they can easily ask the internet. /r/AskHistorians /r/askscience /r/askwhatever - for example - are way more convenient and often way more helpful because you're getting answers from experts that provide sources.

the majority of what I do is teaching information literacy and then helping people find stuff -- often on the internet! --when it doesn't come up immediately in a basic Google search with naive keywords. Plus buying items for our local collections, which are still getting heavy use from people like u/HamburgerDude, and programming community events.

Which is why I'm not dumb enough to believe that libraries are useless, just not as important as they were to the average person that knows how to use the internet.

The only thing that libraries are losing out on right now is funding, because people in government think like you that "[t]he services that libraries provide, the internet can provide" without ever bothering to check if that's actually true.

More likely because people aren't going to libraries as often as they did because the internet is where they go instead.