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

[sgilmore10]

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

[sgilmore10]

take