You were right to note SRS-TO and SRS-GA are not exactly the same.
T/O DSC-22_30-40-20-20
G/A DSC-22_30-40-90-20
What I read is the TO-SRS will engage with TL at TOGA/FLX + flaps/slats extended
on the ground (with V2 inserted) or 5 sec after liftoff (no V2 inserted).
So, after you lose it through any of the disengagement conditions, you won't get it back.
However, setting TL=TOGA (from some other position) while airborne with flap lever position not in zero, will get you the GA-SRS mode.
then (FCOM)
The SRS GA mode disengages when one of the following occur:
- ‐ At the go-around acceleration altitude (GA ACC ALT), or if ALT* or ALT CST* engages (above 400 ft RA)
- ‐ If the flight crew engages another vertical mode
- ‐ If the selected target altitude is above the aircraft altitude and the flight crew selects a speed: SRS GA reverts to OP CLB
- ‐ If the AP/FD TCAS mode engages upon a RA.
Note: 1. In Engine Out conditions, the SRS GA mode does not automatically disengage at EO ACC ALT.