Replace remaining mixins with composables

[matthew-white]

Vue 3 strongly encourages the use of composables over mixins. Composables can be used in any component, but mixins can only be used within components that use the Options API, not the new Composition API. I've been writing more components using the Composition API, which can be very convenient. However, right now many new components can't be written using the Composition API, simply because they use a mixin that we haven't yet converted to a composable. I've converted a few mixins to composables already, but there are still a few key mixins left to convert. I started working on that during v2022.3, and I'm close to being done, but I haven't finished yet. In particular, I'm not sure whether I should complete #675 before or after converting the request mixin to a composable. But even if we don't convert the request mixin to a composable immediately, I think it'd be good to finish converting the other mixins during v2023.1 in order to continue making progress on this issue.