The core of Relations is relative Ethos. The better it fits, the better.
The enigmatic Observers have the usual Xenophile bonus.
Aside from the ethics, there are quests. Enigmatic Observers will ask for one of your pops for thier "Species Preserve" project.
I heard they can ask you for "bioscans" later.
They generally ask you to do stuff that they would do themself otherwise (cleansing colonies nearby/holy worlds/tomb worlds). If you do: +100 Realtionship. If you don't -50 I think (does not seem to get them to declare war on you).
If FE end up Patronizing, they can give you gifts.
Enigmatic Observers are the most interesting to like you: They can end up giving you resources and even FE ships with lower tier equipment.
But keepts of knowledge might give you tech.