export.export_raw does not write fids information in SET file #10529
Description
Describe the bug
export_raw does not exports fids information of SET files.
Steps to reproduce
>>> import mne
>>> import os
>>> file = "/Users/cmadjar/Desktop/eeg_test_data/2022-04-13/003_BaDaNovel_Rutgers_SM.set"
>>> raw = mne.io.read_raw_eeglab(input_fname=file, preload=False, verbose=True)
Reading /Users/cmadjar/Documents/MATLAB/eeglab2022.0/sample_data/eeglab_data.fdt
>>> raw.get_montage()
<DigMontage | 0 extras (headshape), 0 HPIs, 3 fiducials, 129 channels>
>>> raw.get_montage().get_positions()
... 'coord_frame': 'head', 'nasion': array([ 6.34122109e-16, 1.03559999e+01, -2.69400001e+00]), 'lpa': array([-6.71199989, 0.046 , -3.71199989]), 'rpa': array([ 6.71199989, 0.046 , -3.71199989]), 'hsp': None, 'hpi': None
>>> out_file = "/Users/cmadjar/Desktop/eeg_test_data/2022-04-13/test.set"
>>> mne.export.export_raw(fname=out_file, raw=raw, fmt='eeglab')
Reading 0 ... 340244 = 0.000 ... 680.488 secs...
>>> raw_test = mne.io.read_raw_eeglab(input_fname=out_file, preload=False, verbose=True)
>>> raw_test.get_montage()
<DigMontage | 0 extras (headshape), 0 HPIs, 0 fiducials, 129 channels> # <---------------------
>>> raw_test.get_montage().get_positions()
... 'coord_frame': 'head', 'nasion': None, 'lpa': None, 'rpa': None, 'hsp': None, 'hpi': None # <---------------------Expected results
The fids should be exported to the SET file when creating the file from raw.
Actual results
See lines above flagged with # <---------------------
Additional information
Built mne using the following commit: 706dd3a
>>> mne.sys_info()
Platform: macOS-11.3-x86_64-i386-64bit
Python: 3.9.12 (main, Mar 26 2022, 15:52:10) [Clang 13.0.0 (clang-1300.0.29.30)]
Executable: /Users/cmadjar/Development/python_venv/python_intel_3.9.4/eeg2bids_py3.9.12/bin/python
CPU: i386: 8 cores
Memory: Unavailable (requires "psutil" package)
mne: 1.1.dev0
numpy: 1.21.5 {blas=openblas, lapack=openblas}
scipy: 1.8.0
matplotlib: 3.5.1 {backend=MacOSX}
sklearn: 1.0.2
numba: 0.55.1
nibabel: Not found
nilearn: Not found
dipy: Not found
cupy: Not found
pandas: 1.4.1
pyvista: Not found
pyvistaqt: Not found
ipyvtklink: Not found
vtk: Not found
qtpy: Not found
ipympl: Not found
pyqtgraph: Not found
pooch: v1.6.0
mne_bids: 0.10
mne_nirs: Not found
mne_features: 0.2
mne_qt_browser: Not found
mne_connectivity: Not found
Related to #10474