does cdream feel embarassed to have never realized that he proposed to ctechno on their duel? How does bad feel about the engagement?
hmm something important to think about is the whole timeline of events. if dream had found out he accidentally proposed to techno during their duel pretty soon after it happened, then, yeah he would've felt embarrassed.
but he finds out post-prison. he's not in prison as long as he was in canon, but he's still in there for a while, and it takes time for techno to get him out. so, he finds out post-prison, and he's not embarrassed per say, he's just... baffled. he doesn't get why techno never broke off the engagement. he doesn't get why techno kept trying. he doesn't get why techno cared.
the whole concept of techno actually wanting the engagement just doesn't make sense in dream's mind. it won't make sense for a long time.
bad feels pretty good about the engagement lol. at the beginning, he was just really happy for dream (dream assumed he was just proud of him for doing his best in the duel ๐ญ). he's also relieved by the end of it. he's relieved someone had the means to get dream out of prison. he's relieved dream still has someone who he can rely on to support him. I'd say overall he's always had pretty favorable views of the engagement.