Xanathar’s Guide to Everything "expands on the spellcasting rules presented in the Player’s Handbook and Dungeon Master’s Guide, providing…new options", including the ability to identify spells.
Identifying A Spell
Sometimes a character wants to identify a spell that someone else is casting or that was already cast. To do so, a character can use their reaction to identify a spell as it’s being cast, or they can use an action on their turn to identify a spell by its effect after it is cast.
If the character perceived the casting, the spell’s effect, or both, the character can make an Intelligence (Arcana) check with the reaction or action. The DC equals 15 + the spell’s level. If the spell is cast as a class spell and the character is a member of that class, the check is made with advantage.
This Intelligence (Arcana) check represents the fact that identifying a spell requires a quick mind and familiarity with the theory and practice of casting.
Supposing a spell is successfully "identified", what information is actually conveyed?
The minimum required would seem to be the name of the spell, which is implied by the term "identify". But if a successful check represents that the character is "familiar with the theory and practice of casting," is there more?
Can a character successful at identifying a spell place it on a spell list? For example, ‘that human just cast Hellish Rebuke; that is on the warlock list only, so they are likely to be a warlock.’
Does a character successful at identifying a spell know the complete description of the spell?
For example, "Bob’s been acting strange lately."
"I agree." [to DM] "I’d like to attempt to identify a spell by its effect after it is cast." [succeeds] "Oh, he’s under a Charm Person spell. [Looks up spell] "Well, that has a duration of one hour, so we just need to get him away from other people for a while and then he can tell us who he was charmed by."
Assuming XGtE is used, does this imply RAW that any character of Int 10 potentially has encyclopedic knowledge of every spell of up to 5th level?
Caveats for Potential Answers: I am fully aware that I can invoke Rule 0 and decide how much characters know and don’t know. I am asking whether there is any RAW about this issue outside the passage cited. Even official statements about how much of the PHB is character knowledge (as opposed to player knowledge) could provide useful context.
I am a fairly experienced GM and understand the implications of assuming more or less knowledge of the world by characters. I am not asking for this type of response, in part as it could be opinion-based. Expounding on what different levels of information means for worldbuilding will not be considered ‘answering the question’ from my perspective.