Do the Horrorterrors really care about Sburb sessions at all, or do they just want each different session to end as quickly as possible so its not taking up as much space in the furthest ring.

They’re actually the forces that are Against Creation, in a normal SBURB Session they are the influence opposite of Skaia that conspires with Derse to prevent the creation of the Genesis Frog. They will still offer advice to Dersite Players though, as chaotic, eldritch beings do, kind of incomprehensible in their true intentions. That being said, in-Canon they start getting murdered by LE’s mouth beams so they are more friendly towards the Players, and Rose and Feferi have some personal connection to them, so they’re double chill.