The common log format is used by the Mendix Cloud in the Access Logs (see below the Log section of a Cloud node). I would suggest to let some infrastructural component generate logs like these and not custom build this in Mendix. On what infrastructure are you running?
There are many logging modules available on marketplace. have you explored them?
https://marketplace.mendix.com/link/component/159/CAPE-Groep-B.V./Logging-Module
for logging towards services you can use
https://marketplace.mendix.com/link/component/118920/JAM-IT/Log-to-Papertrail
https://marketplace.mendix.com/link/component/118923/JAM-IT/Log-to-Splunk
furthermore if you want to have your own logging styles, collection then you can make a java action in which you can generalize the params as you like and in there you can connect you external services
You need to use the log message component in the studio code. Here's an example https://www.youtube.com/watch?v=D8d0GqG257c
It depends on what type of installation you use for your environment, if it's private cloud, you can filter the logs in the portal.
If mendix is private cloud in a kubernetes and the load balance installation and you are using ingress-nginx you can get these logs from the pod ingress-nginx-controller
X8X.13.X9.XXX - - [28/Jun/2024:20:01:16 +0000] "POST /xas/ HTTP/1.1" 200 601 "https://xxx-xxx.com" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/126.0.0.0 Safari/537.36" 1108 0.005 [xxxxxxx-dev-xxxxxxxx-mendix-app] [] 172.30.211.156:8080 601 0.005 200