Guildford used to be served by more TOCs, rather than being so SWR centric. I believe Southern and Cross Country services used to call there. I also think FCC included Guildford on the Thameslink maps with an eye to going there, but not sure if they ever did.
Nowadays though yes it's nearly all SWR with a few GWR services on the North Downs Line, which does make it a bit of an oddity to be managed by NR.
Cross Country was only a token two trains per day, other than during diversions when the normal route via Basingstoke and Winchester is closed. (Those diversions still occur regularly.)
Southern used to have regular trains from/to Victoria via the New Line, Epsom and West Croydon. IIRC the final vestiges of those went during COVID (not sure of that though).
Thameslink services were certainly intended, but I don't recall if they ever ran. If they did, it wasn't for long.
Current typical off-peak usage is
GWR 4tph Reading to or from Gatwick
SWR 6tph Waterloo to or from Portsmouth or Haslemere
& 6tph Waterloo via New Line (3 arriving, 3 departing)
So arguably about 75% SWR and 25% GWR, though SWR will have a rather higher proportion of passenger numbers, and more peak extras.