Damage/Melee bonuses on Asari Duelist?

The bonus from backlash requires it to be broken to get the full effect, It is terrible. If you flicker it without taking damage you get no bonus, you have to almost break the aegis, then charge, than melee,

If you break the aegis you get stunned, which shortens the duration to less than you need to charge melee.
If you aren't close enough the aegis aftermath will expire before you can land the melee.
Unless you can get enemies to 99% break the aegis while it is flickering on you won't get a useful bonus and lose the charge bonus.

Don't take backlash to rank six under any circumstance, both upgrades are competing for the worst use of skill points in the game. They would suck if they were 4 point upgrades.

"scaled to the damage absorbed by the aegis"

This scales linear.
If you deplete 90% of the aegis health you get 27%
If you deplete 50% of the aegis's health you get 15% melee
If you deplete 0% of it's health you get 0% bonus
If you fully deplete the aegis you get 30% but are stunned for the beginning of it's duration and can't land two sword melee attacks with whats left.

This is also true for the other shield resurgence upgrade.
You get 50% shields over 3 seconds if the aegis fully breaks, ~17% per second
50 aegis damage gives you 25% shields over 3 seconds. ~8% per second.

Both upgrades are terrible, they give almost nothing, and have anti-synergy with biotic warrior, you suffer longer duration from actually using the aegis for a weaker bonus than biotic warrior gives for free.