I would not considered myself an expect on Checkmk, but I suspect the issue is that you are still the root user inside the docker image and not the site user. Try switching to the site user and running the cmk-update-config command again.
For me my site is called “cmk”
root@checkmk-ix-chart-79587f547c-f8dfp:/# whoami
root
root@checkmk-ix-chart-79587f547c-f8dfp:/# cmk-update-config -vvv --debug
bash: cmk-update-config: command not found
root@checkmk-ix-chart-79587f547c-f8dfp:/# omd sites
SITE VERSION COMMENTS
cmk 2.2.0p3.cre default version
root@checkmk-ix-chart-79587f547c-f8dfp:/# su cmk
OMD[cmk]:~$ which cmk-update-config
/omd/sites/cmk/bin/cmk-update-config
OMD[cmk]:~$