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For LinAlg https://eigen.tuxfamily.org/ is pretty popular. For speech signal processing one option is https://github.com/sp-nitech/SPTK
There are C++ libraries that deal with linear algebra and tensors that are able to produce fully vectorized code without requiring you to mess around with SIMD intrinsics. See, for instance, fastor, blaze, eigen and the huge Trillinos set of packages. C++ is very widely used when it comes to scientific HPC applications. All you need to do is google search or better yet, join r/cpp and r/cpp_questions and start asking away for the things you need. The C++ community is very welcoming and full of experts that will be able to help you.
The first thing you need to realize is that there is no standard package manager in C++. There is also no standardized build system. There are, though, very popular tools that most users would recommend. For package managing, use either Conan or vcpkg and CMake as the build system (note that these package managers can be integrated with CMake)
Again, there is no standard testing suite so you would have to pick a third party library (that preferably integrates with your build system). Popular choices are the google test framework and catch2
Again, there is no standard testing suite so you would have to pick a third party library (that preferably integrates with your build system). Popular choices are the google test framework and catch2