Every time you restart Studio, connected to a remote project (Talend Administration Center) and configured with Nexus, the nexus.log file has a warning similar to the following:
2020-03-06 20:40:56,411+0530 WARN [qtp713962441-303] talend-custom-libs-admin org.sonatype.nexus.repository.view.handlers.ExceptionHandler - Illegal operation: PUT /org/talend/libraries/curator-client-2.6/6.0.0/curator-client-2.6-22.214.171.124: org.sonatype.nexus.repository.IllegalOperationException: Repository does not allow updating assets: talend-custom-libs-release
This is as expected. Every time Studio restarts, it has to connect to the Nexus server and sync all of the libraries from .m2.
The cycle repeats for all of the Studio libraries present in .m2 and is synced based on the User Libraries configuration specified in the Talend Administration Center and thus Studio.
From the Nexus side, the warnings you are seeing are thrown because libraries might already exist. However, Studio does not upload the same libraries repeatedly in Nexus even though the logs show these warnings.
You can safely ignore these warnings.
The curator-client-2.6.0 JAR file appears in the nexus.log after starting Studio connecting to Talend Administration Center.
Notice that the same JAR exists in Nexus. However, it has a different time stamp than the nexus.log.
This means even though the nexus.log is showing you those JARs, because Studio loads them during startup and checks with Nexus to manage the sync, the JARs already available in Nexus are not overwritten. Only the new JARs are uploaded.