Pessimistic - BA codeshare on some existing routes - maybe Loganair/Blue Islands? But not sure how that would benefit BA, the only obvious connections being to Aer Lingus via DUB/MAN(assuming the latter goes ahead).
Optimistic - BA Cityflyer flying some weekend sun routes next summer as they have from other airports - ALC/AGP/PMI/FAO, possibly Greece too?
Up in the clouds - BA Cityflyer basing a few E170/190's flying a mix of European city and sun routes.
Regarding the second scenario, while they'll never be able to offer LCC fares, BACF are probably best placed for flying any longer routes at least off the current runway - their LCY spec (i.e. powerful) E-Jets manage LCY-JSI and similar non stop. Believe they are limited to ~75-80 seats or so, but the 200m runway advantage at SOU vs LCY would probably allow a full 98 passengers on their E190. In fact, I remember it being quoted that FlyLolo were limited to 97 seats on the Flybe E195 which would support this assumption.
Looking at the third it initially seems absurd, but business travel is predicted to recover very slowly BACF may find an excess of capacity at LCY, even accounting for the leisure routes that have grown in recent years there. Outside of SOU there are not many airports that do not have any significant LCC competition on the main european routes, and the runway length works in its favour in this sense to maintain this. In this purely hypothetical scenario, I can't see them not wanting a slice of the major domestic and Irish routes - EDI, GLA, BHD, DUB so it could spell bad news for the likes of Loganair and Eastern.