So, my guess is that this Mika girl is somehow related to how Watanabe became the way she is (like, seeing herself as a background character, not wanting to 'ruin' the yuri). I think the her wish was related to that as well- like, obviously 'the world' refers to the school and friends she's made. So when she says she doesn't want it to be destroyed, my theory is that in the past, something happened with this 'Mika' girl that 'destroyed' her world (i.e. school, friends, whatever) that's somehow traumatized Watanabe and made her compensate by casting herself as a side character and avoiding making friends/having feelings for anyone as a defense mechanism.
TLDR: I think that Watanabe's whole obsession with perfect, pure yuri and stopping anything from soiling it (especially when she freaks out about liking Yoshioka) is actually more about keeping herself safe from being hurt again by separating herself or putting up a wall between herself and her peers (seeing herself as a mob, for instance- I've actually coped in a similar way in the past, deciding I'd be a 'side character' to keep from being hurt again).
That's just my personal theory, haha.