I don't know for sure about the Rolls Trent, but on the GEnx, the EICAS engine surge indication means that a continuous or multiple stall condition exists (three or more surge/stall events within 30 seconds) - it would not be displayed for a single surge/recovery.
I'd be mildly surprised if the Trent 1000 logic is meaningfully different.
In that case, the FADEC logic in theory would set a fixed bleed schedule to partially recover the engine albeit with increased EGT (needing to be monitored).
In actuality it's a fail safe condition limited by the capability of the turbine to sustain the increase in temperature over time
I have no idea if this is the subject of the OP nor if this applies to any specific engine mentioned in this thread above.