Gawyn made his own choices with his eyes wide open to the consequences of his actions with the rings. He functionally committed suicide regardless of the outcome of the duel with Demandred.
I completely agree, but the circumstances which contributed to his decision had a lot to do with his recent close association with her. Gawyn is proud and stupid, but without his warder bond and the Bloodknife doohickeys he might have had the sense to appreciate the vast difference in their abilities, and merely shook his fist impotently from the Andoran section of the battlefield. He'd have been commanding troops under adult supervision, with the usual WoT issues of commanders not being allowed to risk themselves.
I would go so far as to call Egwene's inadvertent contribution to the circumstances of Gawyn's death a net gain for the good guys, because his situation at Tarmon Gaidon removed him from the chain of command and expedited Mat taking over for the corrupted Great Captains. Elayne might not have been so willing to go to him, if she had her favorite brother & First Prince of the Sword to take over for Bashere.
Arguably, if anyone committed rape in that event, it would be Egwene. Desire is not consent (on Gawyn's part), and Egwene is the only one who had a choice of about being there. If she had not been engaging in expressly forbidden activity, she would not have been in a position to violate Gawyn's sexual privacy. If Tylin raped Mat, Egwene raped Gawyn.
In terms of Gawyn's path being somewhat steered by his association with Egwene. Certainly his actions were effected by interactions with many characters, Siuan and Elayne and Elaida drove him down this path more than even Egwene IMO. Ultimately if Elayne hadn't chosen to go to Falme and Siuan hadn't been dismissive of him during her various scheming he would not have been in the situation to make a lot of poor choices. Egwene' role in his final decision should have had the opposite effect in him IMO ... how can you put the person you supposedly love in the situation he ended up placing Egwene in? He knew the consequences his death would have on Egwene yet he knowingly put the rings on and marched off to his own death. Ultimately, he drove Egwene to her death as well, her final actions were dramatically effected by his death.
I'd forgotten Lan had gotten the ter'angreal off Galad.
There simply was no rape. Gawyn, to your point, had no agency. Egwene was a consenting adult. The only awkwardness here is that Egwene was actually trapped and essentially had no way of avoiding what happened in his dream. But she clearly didn't have regret for the actions she engaged in and never felt "taken advantage of"
