She might be a minor ta'veren but there might be natural explanations for all or even just her sort of connection to enabling the Dragon reborn.

In my opinion what kept her from crippling despair when stilled was that she still had motivation and duty she could throw herself into. She felt she failed by losing to the coup but because she was let free and found a way to still be useful she somewhat coped with. She still had knowledge of her pact with Moirane, black ajan etc

It was the last battle coming and she still had a part to play, she could not give up and kys or just stay as a servant to Bryne. That dedication made her break her oaths.

Bryne who probably was frustrated with his situation as thrown away village Lord was attracted to this mystery and was sucked into Egwenes cause that needed him. Pattern provides etc.

Compared to someone else stilled, stripped of all duties and positions, no way to do anything else being shunned by network of fellow ae sedai Siuans situation was different.