Refactor ICA Component Labeling GUI Based on MNE-Python API

[adam2392]

We would like to refactor the ICA GUI to use the ICA API provided in MNE-Python. This will rely on the PR to solve the issues raised in: https://github.com/mne-tools/mne-python/issues/9846#issuecomment-1188297439

I'll think about it, for now, I was more inclined towards (1) because it was constrained. Supporting only datasets in BIDS format makes this first version simpler. 

I don't think it's a good idea to have a pop-up GUI to ask the user for a BIDS path, it can be more error-prone and I don't see a reason to save the IC labels in a .tsv sidecar in a BIDS folder if the original data and ICA decomposition are not in the same BIDS folder.

I like option (3) as well, modifying the ICA instance in place makes a lot of sense, and does not entirely make the .tsv redundant as it will also contain the information about who authored the labels (and other information).

Originally posted by @mscheltienne in https://github.com/mne-tools/mne-icalabel/pull/66#discussion_r923864810