Round tripping read/write does not preserve WCS

There are some issues with roundtripping of WCS when using Spectrum1D read and write.

If you create a spectrum 1D with a wcs:
from astropy.wcs import WCS
from specutils import Spectrum1D
import astropy.units as u

wcs = WCS(header={ 'CDELT1': 1, 'CRVAL1': 6562.8, 'CUNIT1': 'Angstrom', 'CTYPE1': 'WAVE', 'RESTFRQ': 1400000000, 'CRPIX1': 25})
spec1d = Spectrum1D(spectral_axis = (1, 2, 3)*u.nm, flux=(1, 2, 3)*u.Jy, wcs=wcs)

Use that wcs to transform the spectral axis:
spec1d.wcs.pixel_to_world(spec1d.spectral_axis).value
output: array([6.5398e-07, 6.5408e-07, 6.5418e-07])

Then write out that Spectrum1D to file:
spec1d.write('test_output.fits')

And it back in (either using Spectrum1D.read OR fits.open. Neither work because the header keywords weren't preserved),
the wcs on the resulting Spectrum1D isn't saved.
spec1d.read('test_output.fits').wcs.pixel_to_world(spec1d.spectral_axis.value).value
output: array([ 2., 3., nan])

This issue was discovered when working on https://github.com/astropy/specutils/issues/905#issuecomment-1811320860 at a hack day with @kelle

Start by reproducing the supplied Spectrum1D WCS example, then inspect Spectrum1D.read, Spectrum1D.write, and the FITS handling used for the round trip. The issue is done when the WCS header information is preserved and pixel_to_world produces the same result before and after writing and reading the file.