Going to re-assign this to Oleg Nenashev, since he appears to be the primary maintainer for the Promoted Builds plugin, and it appears this may have more to do with the Promoted Builds plugin, and the changes in the Config File Provider plugin (I have looked at the changes in the Managed Scripts Plugin from 1.2.4 to 1.3, there doesn't seem to be anything that would break usage, particularly for a single plugin).

The stack trace is completely about Disk Usage plugin. What makes you think it is related?
Anyway, I need to know the version of the Disk Usage plugin on your instance, I doubt it's the newest one

Disk usage plugin 0.28

On Tuesday I updated Jenkins, and the following plugins from the previous latest versions as of Monday December 19:
Config File Provider (2.13 -> 2.15.1)
Managed Scripts (1.2.4 -> 1.3)
Email extension (2.52 -> 2.53)
Github API plugin (1.80 -> 1.82)
JIRA Plugin (2.2.1 -> 2.3)

Prior to that update, build promotions using managed scripts worked; after, they hung. I performed a careful downgrade of just the Config File Provider and Managed scripts plugins, and the build promotions that use managed scripts work once again. So, I don't know if it is the promoted builds plugin or disk usage plugin that doesn't agree with the updated Config File Provider/Managed Scripts plugins, but that exception definitely does not occur after downgrading those plugins.

the only dependency between the promotion plugin and the config-file-provider/managed scripts plugins, is via the job-dsl plugin. And there is an open PR to solve the issue (JENKINS-39769): https://github.com/jenkinsci/job-dsl-plugin/pull/951

I don't have the job-dsl plugin installed.

So the failing codeline is here: https://github.com/jenkinsci/disk-usage-plugin/blob/disk-usage-0.28/src/main/java/hudson/plugins/disk_usage/DiskUsageProperty.java#L342. Promoted Build's Job Property is an ItemGroup (https://github.com/jenkinsci/promoted-builds-plugin/blob/master/src/main/java/hudson/plugins/promoted_builds/JobPropertyImpl.java#L54), hence it can be legitimately returned in the owner.getParent() call.

DiskUsage plugin performs the invalid and unchecked class cast, hence it is a root cause of the issue. Even if the issue appears during the upgrade of other plugins, Disk Usage Plugin is the one to be fixed.

Reassigned the plugin to lvotypkova, who is a maintainer of the Disk Usage plugin

I have a new stack trace, after again upgrading to Config File Provider Plugin version 2.15.5 (previously upgraded to Config File provider version 2.15.1, which is now flagged as "DO NOT INSTALL" due to issues with Managed scripts/configs). This time the promotion fails quickly rather than endlessly running, and the exception now appears in the UI as follows:
FATAL: can not determine current context/parent for: MyJob/promotion of type class hudson.plugins.promoted_builds.JobPropertyImpl
java.lang.IllegalArgumentException: can not determine current context/parent for: MyJob/promotion of type class hudson.plugins.promoted_builds.JobPropertyImpl
at org.jenkinsci.plugins.configfiles.ConfigFiles.getByIdOrNull(ConfigFiles.java:114)
at org.jenkinsci.plugins.configfiles.ConfigFiles.getByIdOrNull(ConfigFiles.java:140)
at org.jenkinsci.plugins.configfiles.ConfigFiles.getByIdOrNull(ConfigFiles.java:164)
at org.jenkinsci.plugins.managedscripts.PowerShellBuildStep.getContents(PowerShellBuildStep.java:126)
at hudson.tasks.CommandInterpreter.createScriptFile(CommandInterpreter.java:161)
at hudson.tasks.CommandInterpreter.perform(CommandInterpreter.java:93)
at hudson.tasks.CommandInterpreter.perform(CommandInterpreter.java:65)
at hudson.plugins.promoted_builds.Promotion$RunnerImpl.build(Promotion.java:405)
at hudson.plugins.promoted_builds.Promotion$RunnerImpl.doRun(Promotion.java:347)
at hudson.model.AbstractBuild$AbstractBuildExecution.run(AbstractBuild.java:534)
at hudson.model.Run.execute(Run.java:1729)
at hudson.model.Run.run(Run.java:1688)
at hudson.plugins.promoted_builds.Promotion.run(Promotion.java:286)
at hudson.model.ResourceController.execute(ResourceController.java:98)
at hudson.model.Executor.run(Executor.java:404)

Linking, because symptoms match

Code changed in jenkins
User: Lucie Votypkova
Path:
pom.xml
src/test/java/hudson/plugins/disk_usage/integration/DiskUsagePropertyTest.java
http://jenkins-ci.org/commit/disk-usage-plugin/5842185ddfcbfe9cec035dba3ed20a623ef1d60b
Log:
Reproduce issue JENKINS-40728