It's a common mistake that people think that HTTP implementations can't be unit tested too, but the truth is a bit more complicated. These libraries are essentially a wire protocol and people think of them as 'wire-protocol' instead of 'wire, protocol'. If you think of it instead as a codec with IO, then you write the codec separately and you can fully test the codec without mocking any IO at all.
It's nearly tautological that code that is written to be unit tested can be unit tested, and code that isn't cannot be. And because people want to get their code 'working' and then prove that it works, they are battling uphill to get good tests written, because good tests can't be written. And then some people use this as confirmation bias for why they shouldn't have to write tests.
Don’t confuse how it’s done with what is done.
People get suck a kick out of categorizing their tests, I honestly find that funny.
Can you run it easily before you commit code to a unit, without a dedicated setup? Yes, then it's a unit test to me.
If it was me I wouldn't call it "something" test at all. It's just automated tests. The rest is mostly BS.
If you have to test scenarios in which other dependencies are needed, then you must move up the testing pyramid. That serves to put in check the expectations of what each type of test should accomplish, and when to execute those tests.
This differentiation is quite pointless though. If you can spawn the dependency in memory at no cost then why not.
Also not using dependencies is not the point of a unit test. Almost everything has dependencies.