What information is supplied to sites when logging in with Steam OpenID?

According to the Valve Software Wiki. Almost all the info that steam has. Read the options available to the sites that use this API here: https://developer.valvesoftware.com/wiki/Steam_Web_API

According to the read-me on SteamAuthentication's GitHub page:

SteamAuthentication is a basic set of PHP files that enable users to login using their steam account to view protected content on your website. it creates a session using their steamid as the sessionID and checks for the session when a user visits the page. It also includes a file which allows you to use their profile information such as their avatar and online status.

I dont know if there is a system in place to see what you share, but I seem to recall that I had to confirm, much like Google's system, when I logged on to the Terraria site with Steam.

Linked from the Wiki's GetPlayerSummeries. The Private Section:

realname
    The player's "Real Name", if they have set it.
primaryclanid
    The player's primary group, as configured in their Steam Community profile.
timecreated
    The time the player's account was created.
gameid
    If the user is currently in-game, this value will be returned and set to the gameid of that game.
gameserverip
    The ip and port of the game server the user is currently playing on, if they are playing on-line in a game using Steam matchmaking. Otherwise will be set to "0.0.0.0:0".
gameextrainfo
    If the user is currently in-game, this will be the name of the game they are playing. This may be the name of a non-Steam game shortcut.
cityid
    This value will be removed in a future update (see loccityid)
loccountrycode
    If set on the user's Steam Community profile, The user's country of residence, 2-character ISO country code
locstatecode
    If set on the user's Steam Community profile, The user's state of residence
loccityid
    An internal code indicating the user's city of residence. A future update will provide this data in a more useful way.
    steam_location gem/package makes player location data readable for output.