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> typedef uint16_t uint16;

does adding that little "_t" hurt you that much ? think that now every programmer reading your code will wonder "hmm... what is that uint16 type ? is it equivalent to uint16_t ? is it some weird macro designed to accomodate 1990 compilers ?" etc etc.

> const char *fileName

for the love of all things holy, use std::string_view for non-performance-critical stuff like this.

More generally, the only remotely C++-like thing in your code is the use of std::vector. The rest is honestly more C than C++. This shows for instance in SampleChannelFractional with that ugly #if 0. Proper C++ design would have SampleChannelFractional be instead a function object that you could pass as template argument: this way, the user can choose which implementation he wants without requiring a recompilation, and without indirection cost.

In addition, if you change some parts of your code, the C++ compiler will be able to check both code paths directly.

That is :

    struct LinearSampleChannelFractional
    {
      float operator()(const std::vector<float>& input
                     , float sampleFloat
                     , uint16 channel
                     , uint16 numChannels)  
      {
        // your linear implementation here
      }
    };
    
    struct CubicSampleChannelFractional
    {
    
      float operator()(const std::vector<float>& input
                     , float sampleFloat
                     , uint16 channel
                     , uint16 numChannels)  
      {
        // your cubic implementation here
      }
     
      private:
         float CubicHermite (float A, float B, float C, float D, float t)
         { 
            // encapsulate it here: 
            // the rest of your code does not care about this function.
         }
    };
    
    // First modification: pass Fractional as template argument
    template<typename Fractional>
    void TimeAdjust (...)
    {
      // replace SampleChannelFractional: 
      output[...] = Fractional{}(input, srcSampleFloat, channel, numChannels);
    }

    template<typename Fractional>
    void SplatGrainToOutput (...)
    {
      // same
      output[...] = Fractional{}(...);
    }
    
    // Second modification: refactor this in a Granulator class of some sorts...
    // and use the standard C++ naming convention    
    template<typename Fractional>
    class granulator
    {
      public:        
        void time_adjust (...)
        { 
          // uses the class template argument
          output[...] = Fractional{}(input, srcSampleFloat, channel, numChannels);
        }
        
        void splat_grain_to_output (...)
        {
          // same
          output[...] = Fractional{}(...);
        }
        
        void granular_time_pitch_adjust (...)
        {
           // ... splat_grain_to_output(...)
        }
    
    int main()
    {
        // now both kinds can be used at the same time in your code, and both will be 
        // just as efficient as with the #if 1 ; for instance the choice 
        // of the granulator to use can then be part of a configuration option 
        // in a GUI software
        constexpr granulator<cubic_sample_channel_fractional> gran1;
        gran1.time_adjust(source, out, numChannels, 0.7f);
        
        constexpr granulator<linear_sample_channel_fractional> gran2;
        gran2.time_adjust(source, out, numChannels, 0.7f);
    }