[Crossover] I'm Definitely Not Galahad!

Galahad, Galahad, Galahad... For a long time, everyone called her by that name, but she knew very well she wasn't the real Galahad. Since there was no "Galahad" in this timeline, she was only filling in an empty space. She felt there were so many things she couldn't accept, but she didn't know how to change them. She'd had enough of living one step at a time. Being summoned as a Heroic Spirit was fine. Saving humanity was fine. Even seeing so many familiar faces was fine. But she couldn't see the person she most wanted to meet. So she kept chasing after them. "If I save humanity, I'll be able to see that person again, right?" A voice answered from the void: "That's right." - So the young lady who isn't called Galahad is working hard to save humanity again today! Gudako: That is, as long as you stop turning things into a love-triangle battle with Mordred, Galahad! 1. The pairing is undecided, but no pairing is the most likely outcome. 2. There are many romanceable characters, including Gudako, but don't worry, there are no boys for now! 3. There is no Galahad in this world! 4. Though summoned as a Heroic Spirit, the pseudo-Galahad has the ability to transmigrate across time and space, like Miyamoto Musashi, because she isn't from this world. 5. The Fate universe is enormous, so there may be errors. Please point them out. This is intended as a Fate/Grand Order First Arc fanfic. I haven't read the second arc yet, so I hope the official story doesn't prove me wrong. 6. Even if it does, this is just a parallel world!