1. PostgreSQL 13 Official Documentation, Chapter 26. Backup and Restore, Section 26.3.1. Setting Up WAL Archiving.
"To enable WAL archiving, set the wallevel configuration parameter to replica or higher, archivemode to on, and specify the shell command to use in archivecommand." This explicitly states replica as the minimum requirement.
2. PostgreSQL 13 Official Documentation, Chapter 19. Server Configuration, Section 19.5.1. Settings.
"wallevel determines how much information is written to the WAL. The default value is replica. Possible values are minimal, replica, and logical." It further clarifies: "replica writes enough data to support WAL archiving and replication..." and "minimal removes all logging except the information required to recover from a crash or an immediate shutdown."
3. PostgreSQL 13 Official Documentation, Appendix F. Release Notes, Section F.28. Release 9.6.
"Merge wallevel settings archive and hotstandby into a new setting replica (Simon Riggs, Robert Haas)." This confirms that archive is an outdated setting from before version 9.6.