I wasn't even rooting for Fuuka and Asahi, but it's still sad. Of course I feel bad for Fuuka, but I also feel like she's giving up way too soon after hanging on for years? But I suppose it's maybe in character for her, who is said to go into and out of relationships quickly.
I don't think Fuuka gave up too soon. As you said, she's known, and been in love with, Asahi for YEARS. The only reason she actually tried to make her move is that she saw the writing on the wall. She watched how Asahi and Hinako acted around each other and could tell that, even though Asahi and Hinako were both far too naive about love, especially between two women, to really recognize what was happening between them, they were falling for each other, if it hadn't already happened and they just couldn't put a name on the feelings yet. Heck, earlier on the day when Asahi "ran away" to Hinako's house, Asahi mentioned that Hinako was staying home to clean her apartment and Fuuka snarked that nobody asked about Hinako and yet Asahi seems to bring her up even when she isn't around. And then she finds out that she went to Hinako to help her get ready for the date. The fact that she chose her own nail polish color was only a small positive in that for Fuuka. Everything else about Asahi's date preparations was a massive red flag. And even that small positive was still influenced by Hinako because Asahi normally wouldn't bother with nail polish. It's also kind of telling that Asahi didn't tell Fuuka the whole truth about the nail polish. When she asked if it was from Hinako, Asahi replied that she picked it herself. But it was from choices presented to her by Hinako and Hinako bought it for her as a present, so very technically the answer was "yes". The fact that Asahi felt the need to color the truth in that manner suggests that she understood by that point, at least to some degree, that it was her relationship with Hinako that prompted Fuuka to tell her about her feelings after all these years.
There's also the wording Fuuka used when describing what she "expected" from Asahi if they were "going out": "When you're suffering, I want you to rely on me the most." There was a reason Fuuka put that first. The thing that pushed her into confessing and asking Asahi out on this date in the first place was when Asahi "ran away from home" because of her argument with Subaru. And whom did she rely on when she was suffering then? Hinako! Finding out that Asahi also relied on that same person to help her look good for their date, even though she "didn't tell her it was a date" (like that worked), pretty much started the date off with confirmation that it was a lost cause.