cmake-init-conan-example VS small

I haven't really used conan but you should not use the cmake generator, you should use the CMakeDeps and CMakeToolchain generators instead. That might solve your problem, after all there is a reason why the cmake generator is being deprecated. Check this for an example: https://github.com/friendlyanon/cmake-init-conan-example

Use a package manager. This example shows how to use vcpkg to get json-c. You can do the same using Conan as well.

You ought to call Conan before configuring. Take a look at this example.

Conan and vcpkg are the only options. I use them both, depends on what kinds of dependencies I want to pull. vcpkg is easier to setup custom one-off dependencies with using overlay ports, while Conan is faster at things if your profile fits one that has a pre-built binary in CCI. Both are trivial to integrate with a CMake project, see these examples for Conan and vcpkg.

More details in this example project.

I have an example for Conan integration that I'm planning on revisiting, since it was made when I knew less about Conan. If you are interested in a concrete example, you can check it out later.

Integrating with Conan is already pretty straightforward, you just need a short script to glue things together via the Conan provided CMake utility.

You can check out the CI for this example project. It doesn't yet have caching for Conan setup, but Qt has prebuilt binaries in the CCI anyway, so that's not really that big of a deal.

The CMake scripts could definitely use improvement. Here is an example using Conan that also installs fmt. The shell scripts can also be entirely replaced with CMake presets, also examplified in the earlier link.

Or Conan + CMake. In fact, I would much prefer to use Conan in a company environment, but vcpkg is top notch for open source. Not to say Conan is bad at that, not even close, but its features are excellent to get companies to move to package managers.