7-Zip by Igor Pavlov can create zip files, has multi-threading and in my small test, comparing with the "pzip", was both as fast in "real" time and produced smaller file (while using similar amount of CPU but differently distributed between user and sys).

https://www.7-zip.org/download.html

Also, in my example the compression level of Info-Zip that best matched the one in pzip was -3 This can, of course, depend on the set.

    ~/c/measure_pzip$ time 7z -tzip -mx1 a a7.zip /usr/lib/apache2/*

    7-Zip (z) 23.01 (x64) : Copyright (c) 1999-2023 Igor Pavlov : 2023-06-20
     64-bit locale=en_US.UTF-8 Threads:3 OPEN_MAX:1024, ASM

    ...

    real 0m0,074s
    user 0m0,121s
    sys 0m0,014s
    ~/c/measure_pzip$ time ./pzip a-p.zip /usr/lib/apache2/*

    real 0m0,073s
    user 0m0,097s
    sys 0m0,038s
    ~/c/measure_pzip$ time zip -3 -r a-zip.zip /usr/lib/apache2/ >/dev/null

    real 0m0,118s
    user 0m0,114s
    sys 0m0,004s

    ~/c/measure_pzip$ ls -l a*.zip | ./my2
    1576511  a7.zip
    1619733  a-p.zip
    1613607  a-zip.zip