Simpler way of deduplicating code in duplicate checks

[steffahn]

Alternative to #2701

No LLMs were used in this PR 😃

[github-actions]

Dry-run check results

[WARN  rust_team::sync] sync-team is running in dry mode, no changes will be applied.
[INFO  rust_team::sync] synchronizing crates-io
[INFO  rust_team::sync] synchronizing github

[steffahn]

I touched the code some more, resulting in a larger refactor of the duplication checking function,
as well as adding detection for duplicate role assignment (which didn't exist previously, and uses the refactored duplicate detection), as well as validation for roles in alumni.

Since that's a complete rewrite of the PR, it's a new PR (→ #2703); I'm leaving this one as draft [as long as #2701 remains open] for illustrative purposes so my comments in #2701 (comment) still make sense.