Although there is a /usr/bin/apt in macOS Big Sur, there is no documentation available via man page, or command-line switches (-h | --help) that would confirm that it has the same functionality as apt on Linux.
In the past, it seemed to me that the JRE (Java runtime) was bundled with the JDK download, and should be present with your installation of Java 16.0.1. Perhaps not, which may imply that you need that same JRE version installed to satisfy the apt command, or that the apt command may have been blinded by a hardcoded Java version expectation.
Upon performing strings on the /usr/bin/apt application, it does not support the Linux apt command set:
strings /usr/bin/apt | more -r
You may also need to set JAVA_VERSION in your environment.