So far I have not found any function or plugin to add the composers of a song, does anyone know how you can add?
If the composer is in the database (probably attached to a work), Picard should add it automatically. For classical, it will also be the track artist. If the composer isn’t in the database, you can always add it by relating the track to a work (which you may or may not also need to create)
Following up on @psychoadept’s answer, https://musicbrainz.org/doc/How_to_Use_Works has information on how Works work and how to use them and edit them. (Works is the entity type in MB that stores information about composers.)
Im not sure about but I think the issue is that whilst the composer may be set as the track artist unless works have been added for each track and a composer relationship attached to the work then Picard wont recognise the track artist as being a composer it would just add as track artist and nothing else.
This is a good reason for something like the classical flag that has been discussed. If a release is known to be classical, then perhaps the composer can be inferred (by Picard or such) from the track artist (I would think optionally, since there are obviously exceptions).