Leareth's packet of notes isn't very polished and lacks formal textbook features such as an index or page numbers or a clear organization schema, but it does have lots of information on gods, clearly marked with how confident he is in each assessment.
Confident claims: the gods are very large, powerful beings that exist across a number of planes, possibly all of the planes. They have a certain ability to perceive reality, though not from the same angle or at the same level of granularity as mortal beings do, and correspondingly they have fairly different mind-setups and concepts; this leads to the predictable communication difficulties when They deign to talk to mortals, which isn't usually.
Slightly less confident inferences: one of the gods' primary ways of perceiving the world is direct Foresight; they See the various possible paths of the future, and implicitly know what nudges will affect it, the same way humans know how to navigate a crowded room just from vision. This is likely one of the roots of their dislike for rapid change.
The gods' actual values are both hard to infer, since their actions are often very indirect and sometimes not noticeable as interventions at all, and even when they are it's not always possible to tell which god did something and they rarely claim credit. They do seem to care somewhat about human lives - the Star-Eyed was willing to perform what must have been a very costly miracle to make land habitable for her people after the Cataclysm, albeit in exchange for a permanently binding pact with all their descendants - but they're clearly not optimizing for human happiness, or else, well, the world would look pretty different from how it does now.
Probably the biggest single obstacle to useful cooperation between gods and mortals is the communication gap. Gods are cryptic. Some of this is inherent in the kind of being they are, vast and alien, but not all of it, Leareth thinks that if you build a god with the minimal crypticness possible then it would be a lot better.