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^{Transferring comments into an answer.}

Specifying the -l and -L operations when compiling to object files is irrelevant. Some versions of GCC warn about arguments that won't be used because they are link-time arguments, and linking won't be used when you include the -c flag.

The ar command doesn't know what to do with the C compiler's -l and -L arguments (it might have its own uses for the flags; one version of ar accepts but ignores -l).

So, you have to specify the dependencies when you link with the static library. That is the way life has been since the early 70s — that aspect hasn't changed yet. Shared libraries can be built with the dependency information, but not static libraries.

As I understand it, I need to build a shared library and link it in a static way, right?

No. You either need to build and link a shared library as a shared library, or you need to accept that using a static library means you will need to specify other libraries on the command line when you use this library. There are systems to help manage such information; pkg-config is one such. AFAIK, you cannot link a shared library in a 'static way'.