fMRIprep can definitely produce CIFTI files and can do so in both standard and native spaces.
I am surprised that it is possible to get just the GIFTI files. Here's what I get from fMRIprep. Note that the fMRI data is in standard space by default, unless you ask for native space to be provided as well (which I have here):
├── anat
│ ├── sub-219_ses-itbs_desc-aparcaseg_dseg.nii.gz
│ ├── sub-219_ses-itbs_desc-aseg_dseg.nii.gz
│ ├── sub-219_ses-itbs_desc-brain_mask.json
│ ├── sub-219_ses-itbs_desc-brain_mask.nii.gz
│ ├── sub-219_ses-itbs_desc-preproc_T1w.json
│ ├── sub-219_ses-itbs_desc-preproc_T1w.nii.gz
│ ├── sub-219_ses-itbs_dseg.nii.gz
│ ├── sub-219_ses-itbs_from-MNI152NLin2009cAsym_to-T1w_mode-image_xfm.h5
│ ├── sub-219_ses-itbs_from-MNI152NLin6Asym_to-T1w_mode-image_xfm.h5
│ ├── sub-219_ses-itbs_from-T1w_to-MNI152NLin2009cAsym_mode-image_xfm.h5
│ ├── sub-219_ses-itbs_from-T1w_to-MNI152NLin6Asym_mode-image_xfm.h5
│ ├── sub-219_ses-itbs_from-T1w_to-fsnative_mode-image_xfm.txt
│ ├── sub-219_ses-itbs_from-fsnative_to-T1w_mode-image_xfm.txt
│ ├── sub-219_ses-itbs_hemi-L_inflated.surf.gii
│ ├── sub-219_ses-itbs_hemi-L_midthickness.surf.gii
│ ├── sub-219_ses-itbs_hemi-L_pial.surf.gii
│ ├── sub-219_ses-itbs_hemi-L_smoothwm.surf.gii
│ ├── sub-219_ses-itbs_hemi-R_inflated.surf.gii
│ ├── sub-219_ses-itbs_hemi-R_midthickness.surf.gii
│ ├── sub-219_ses-itbs_hemi-R_pial.surf.gii
│ ├── sub-219_ses-itbs_hemi-R_smoothwm.surf.gii
│ ├── sub-219_ses-itbs_label-CSF_probseg.nii.gz
│ ├── sub-219_ses-itbs_label-GM_probseg.nii.gz
│ └── sub-219_ses-itbs_label-WM_probseg.nii.gz
└── func
├── sub-219_ses-itbs_task-rest_run-1_AROMAnoiseICs.csv
├── sub-219_ses-itbs_task-rest_run-1_desc-MELODIC_mixing.tsv
├── sub-219_ses-itbs_task-rest_run-1_desc-confounds_timeseries.json
├── sub-219_ses-itbs_task-rest_run-1_desc-confounds_timeseries.tsv
├── sub-219_ses-itbs_task-rest_run-1_from-T1w_to-scanner_mode-image_xfm.txt
├── sub-219_ses-itbs_task-rest_run-1_from-scanner_to-T1w_mode-image_xfm.txt
├── sub-219_ses-itbs_task-rest_run-1_space-MNI152NLin6Asym_desc-smoothAROMAnonaggr_bold.json
├── sub-219_ses-itbs_task-rest_run-1_space-MNI152NLin6Asym_desc-smoothAROMAnonaggr_bold.nii.gz
├── sub-219_ses-itbs_task-rest_run-1_space-fsLR_den-91k_bold.dtseries.json
├── sub-219_ses-itbs_task-rest_run-1_space-fsLR_den-91k_bold.dtseries.nii
├── sub-219_ses-itbs_task-rest_run-1_space-fsLR_den-91k_bold.json
├── sub-219_ses-itbs_task-rest_run-1_space-fsaverage_hemi-L_bold.func.gii
├── sub-219_ses-itbs_task-rest_run-1_space-fsaverage_hemi-L_bold.json
├── sub-219_ses-itbs_task-rest_run-1_space-fsaverage_hemi-R_bold.func.gii
├── sub-219_ses-itbs_task-rest_run-1_space-fsaverage_hemi-R_bold.json
├── sub-219_ses-itbs_task-rest_run-1_space-fsnative_hemi-L_bold.func.gii
├── sub-219_ses-itbs_task-rest_run-1_space-fsnative_hemi-L_bold.json
├── sub-219_ses-itbs_task-rest_run-1_space-fsnative_hemi-R_bold.func.gii
├── sub-219_ses-itbs_task-rest_run-1_space-fsnative_hemi-R_bold.json
├── sub-219_ses-itbs_task-rest_run-2_AROMAnoiseICs.csv
├── sub-219_ses-itbs_task-rest_run-2_desc-MELODIC_mixing.tsv
├── sub-219_ses-itbs_task-rest_run-2_desc-confounds_timeseries.json
├── sub-219_ses-itbs_task-rest_run-2_desc-confounds_timeseries.tsv
├── sub-219_ses-itbs_task-rest_run-2_from-T1w_to-scanner_mode-image_xfm.txt
├── sub-219_ses-itbs_task-rest_run-2_from-scanner_to-T1w_mode-image_xfm.txt
├── sub-219_ses-itbs_task-rest_run-2_space-MNI152NLin6Asym_desc-smoothAROMAnonaggr_bold.json
├── sub-219_ses-itbs_task-rest_run-2_space-MNI152NLin6Asym_desc-smoothAROMAnonaggr_bold.nii.gz
├── sub-219_ses-itbs_task-rest_run-2_space-fsLR_den-91k_bold.dtseries.json
├── sub-219_ses-itbs_task-rest_run-2_space-fsLR_den-91k_bold.dtseries.nii
├── sub-219_ses-itbs_task-rest_run-2_space-fsLR_den-91k_bold.json
├── sub-219_ses-itbs_task-rest_run-2_space-fsaverage_hemi-L_bold.func.gii
├── sub-219_ses-itbs_task-rest_run-2_space-fsaverage_hemi-L_bold.json
├── sub-219_ses-itbs_task-rest_run-2_space-fsaverage_hemi-R_bold.func.gii
├── sub-219_ses-itbs_task-rest_run-2_space-fsaverage_hemi-R_bold.json
├── sub-219_ses-itbs_task-rest_run-2_space-fsnative_hemi-L_bold.func.gii
├── sub-219_ses-itbs_task-rest_run-2_space-fsnative_hemi-L_bold.json
├── sub-219_ses-itbs_task-rest_run-2_space-fsnative_hemi-R_bold.func.gii
└── sub-219_ses-itbs_task-rest_run-2_space-fsnative_hemi-R_bold.json