Uploading potentially copyrighted material onto Academia.edu On Academia.edu, a user uploaded a Translation Database of Sun Tzu's Art of War, which includes translations as recent as 2020. Alongside it was a Bibliography Document that references all works shown in the former. I’d like to upload a similar document that shows Translations of Laozi’s Tao Te Ching, however I don’t know if this would violate any copyright protection held by the Authors/Publishers.
This site here, presents many translations, some entries consisting of an authors’ text verbatim whereas others either link to a pdf or to a wayback machine page. Seeing as it’s still operating, I’m assuming that TAO hasn’t violated any copyright protection, I’m wondering whether I could include translations appearing in TAO without violating copyright protection. I recognise that for some translations, in the case of Beck
or Muller,  I would need to seek permission in order to include them in the database, however would I need to do this for all translations that are not in public domain?
Laozi's work is not protected by copyright, you are free to provide translations. You cannot freely distribute translations of others.

This site here, presents many translations...Seeing as it’s still operating, I’m assuming that [the site] hasn’t violated any copyright protection

Your assumption is false: The absence of a take-down or prosecution doesn't imply an absence of copyright violation.