Improve public view clarity for club administrators during reapproval/application periods

[julianweng]

Many pain points for club administrators during application season (particularly Fall / new school year) relate to a lack of clarity on what non-members are able to access on the club page. This manifests both during the reapproval process, where clubs are unaware of what changes are visible on the page (it shows the latest version for them versus the latest approved version for non-admin), and during the application process, where club admin sees the "Manage Club" button instead of the "Apply" button.

This associated PR would create a "student/applicant view" mode for club members that allow them to see the page from a non-club member, but authenticated perspective. It would be accessible via an action button on the page visible to club members. Relatedly, it would also revamp the "application_open" field for clubs: it's unclear how club leaders are expected to turn it on and off in the current user flow, so is often outdated as a result. For application required clubs, it should be tied to the existence of an upcoming or active club application, while for open clubs, the request membership button should just always be shown (unless user research shows that there are clubs that actually enforce application cycles but then accept everyone).