The existing options don't seem anywhere as good as existing closed-source software.
Each application was an issue. It contained the résumé and information about the applicant. We had an issue template.
Stages of the process were labels. We'd move the issue around and our discussions would be in comments on the issue. It worked for us really well.
We used GitLab for administration as well.
Only half joking, things happen when one needs them in free software.