The official documentation says

"Participant fields are not included in the Excel/CSV data export, or in the “Data” tab in the session admin." (https://otree.readthedocs.io/en/latest/rounds.html)

However, I have always been able to download participant.vars as they are embedded on the "long" Excel report ("All Apps").

Is the documentation outdated?

Yes now that participant fields are included in the data export, I can remove that, thank you for reporting it :)