[MATLAB] Implement `featherwrite` in terms of `arrow.internal.io.feather.Writer`

### Describe the enhancement requested

Now that #37043 is merged, we can re-implement `featherwrite` in terms of the new `arrow.internal.io.feather.Writer` class. Once this change is made, we can delete the legacy build infrastructure and featherwrite MEX code. 

### Component(s)

MATLAB