Ah, there's a server-mode: https://kopia.io/docs/repository-server/
By default, every user of Kopia repository directly connects to an underlying storage using read-write access. If the users who share the repository do not entirely trust each other, some malicious actors can delete repository data structures, causing data loss for others.
Repository Server allows an instance of Kopia to proxy access to the underlying storage and has Kopia clients proxy all access through it, only requiring a username and password to talk to the server without any knowledge of repository storage credentials.
In repository server mode, each user is limited to seeing their own snapshots and policy manifest without being able to access those from another user account.