After watching "All Our Yesterdays" it would appear that the TOS Enterprise has no problem warping away although it was technically called a "nova".
"Generations" is an odd duck alright. They see the explosion first with the flash at the cabin window. Then they confirm a "quantum implosion" that is sending a "level 12 shockwave" at them that will reach them in "4 minutes, 40 seconds". But interestingly, Riker says that the "star is going to collapse in a matter of minutes." This would suggest that the "level 12 shockwave" is not part of a "supernova" and that the supernova will occur a bit afterwards. The initial "light flash" does seem to be FTL though. Perhaps later when the Veridian star exploded the "immediate" light effect is normal in TNG star explosions?
So we have:
- DS9 "Second Sight" - escape from a supernova is possible, especially at Warp 9.5 but timing is not specified. Is that before star goes supernova (since they are monitoring the star they could predict a supernova and react to it.)
- DS9 "By Inferno's Light" - escape from a supernova not possible, no reason given
- VOY "The Q and the Grey" - escape from a supernova at impulse power is possible if at least 66 AU away. Shockwave is FTL. Subspace shockwave from supernova collapses Voyager's warp field preventing warp escape.
- TOS "All Our Yesterdays" - escape from a "nova" is possible, at maximum warp
- TNG "Generations" - escape from a "level 12" shockwave is possible at warp speed. Unknown if the star went nova or supernova.