Does Enduring Agony increases the damage of bleeding and poison

I'm sure you've figured it out by now, but I'll answer if only to provide one clear answer, combining all the information.

Enduring Agony does not increase the damage per second of bleeding and poison abilities, but it does increase their duration which effectively increases their damage by extending the duration of the DPS effect. For example, an effect of 10 poison damage over 5 seconds is a DPS of 2 damage/second for a total of 10 damage over 5 seconds, but with 1 level in Enduring Agony, the effect lasts 6 seconds (5 * 1.2 = 6), thus dealing 12 damage over 6 seconds. An additional 2 points in this example would yield 14 damage over 7 seconds, etc. It's not going to make or break the amount of damage you deal as the numbers are usually so small.

The more useful aspect is that by increasing the poison and bleeding effect duration, the weakening of the opponent's damage dealt caused by the poison effect and the weakening of the opponent's defense by bleeding are also extended. By extending the bleeding effect, you also extend the window to do more damage with other attacks, leading to a further improvement in damage.

Additionally Enduring Agony also increase the damage of Shadow Flare which, while not devastating towards the end of the game, it also causes a bleed effect and can still be marginally useful against big enemies if all 5 blades hit and can be good if you need to stun some enemies quickly.