[JENKINS-70351] Fix initialization and deprecate obsolete SupportContext

[Dohbedoh]

JENKINS-70351

• Removed the SupportPlugin#postInitialize that happens on plugin startup
• Deprecate the SupportContext that the SupportPlugin#postInitialize is setting as it is obsolete / unused since 5905c4f.
• Add an @Initializer(after = InitMilestone.EXTENSIONS_AUGMENTED, before = InitMilestone.SYSTEM_CONFIG_LOADED) to the CustomLogs.CustomLogHandler. For some reason, this was done via Component#start(SupportContext) though not related to the SupportContext.

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