All calls made by the add-on to a site should be traceable, to assist in debugging and understanding behaviour of the add-on.
This can be done by adding logging or collecting of metrics. In case of metrics it should be the function called and not the url called for metrics.
Logging of HTTP requests would have helped me verify that caused the errors that I saw. In particular:
"Failed to synchronize build 197 of master: null" in the Jira log does not say which project's master branch it was trying to synchronize.
The REST API of Jenkins does not output all properties of actions by default, so I initially got the false impression that the problematic "environment" property was not even part of the response. This could have been avoided if the add-on had also logged the query parameters of the HTTP requests that it sent to Jenkins.
To avoid bloating the log files, perhaps the detailed logging could be automatically activated only when errors occur.
Completely agree, the behaviour should add useable data and not just bloat the logs.