I thought Linux is POSIX-compliant, yet some POSIX commands are not found

I wanted to write a small shell script for Linux and other UNIX systems (probably OSX). And also, why not keep things platform-independent out of principle, right? So I went with a #!/bin/sh shebang and one part of my script is supposed to compress a string so I thought I'd just have a look which is the POSIX default utility to compress strings or streams. Unsurprisingly, neither tar or gzip were listed at https://pubs.opengroup.org/onlinepubs/9699919799/idx/utilities.html . But what I did not expect: the listed compress was not installed on my Debian 11 Bullseye system! So I cannot even rely on POSIX commands being available on all so called POSIX-compliant systems? Did I make a mistake somewhere?