One question- What version of fMRIPrep did you use?
If you used v21.0.0 or v21.0.1, there might be a double-unwarping issue affecting the optimally combined data fMRIPrep generates, but not the individual, preprocessed echos. In that case you would probably want to combine the individual echos and then apply the transforms afterwards, rather than use the standard-space combined data that are available. You can look at Potential "double-unwarping" bug in bold_to_t1w_transform when running fmriprep on multi-echo data · Issue #2727 · nipreps/fmriprep · GitHub for more info.
This is totally valid. We (the tedana devs) are actually in the process of adding information about that kind of denoising into our documentation. If you want more info about our thoughts on it, you can take a look at https://github.com/ME-ICA/tedana/pull/823. The considerations for including tedana’s ICA components in your GLM are basically the same as if you used ICA-AROMA for denoising and wanted to regress out its noise components. I believe there are a few questions about ICA-AROMA on NeuroStars that would be relevant to you, such as ICA-AROMA and Head Motion Regression or Aggressive vs nonaggressive denoising.
Additionally, @handwerker might have some insight into how best to do this.
I don’t think there’s an issue with the nature of the ICA components (i.e., the fact that they’re classified based on TE [in]dependence).
I think your primary concern should be about confound regressor independence. If you’re going to include nuisance regressors like motion parameters in your GLM, then you might want to orthogonalized the ICA components w.r.t. the other nuisance regressors, or vice versa.
tedana also has an option (--tedort) to orthogonalize the rejected ICA components w.r.t. the accepted ICA components, resulting in what we’ve called “pure evil” components. It might be worth considering.