refactor(controller): encapsulate context cancellation logic

[rogercoll]

When the Controller is used as a library (e.g., within the OpenTelemetry Collector), the context passed to Start() is often long-lived and not cancelled when the component is shut down. Previously, this caused background tasks, such as startTraceHandling and trace handling loops, to leak or persist after Shutdown() was called.

This change moves the creation of a cancellable context inside Controller.Start(). The Controller now manages its own lifecycle using an internal CancelFunc.

Differently than the profiler's main, the collectors start/shutdown workflow does not explicitly cancel the Start context (or SIGTERM cancellation).

[florianl]

To avoid shadowing conflicts, the new context should be named differently to the context that is given as argument.

[rogercoll]

In this case we intentionally want to override the parent context and prevent its use further down the function. I think that reusing ctx here aligns with Google best practices (“It’s OK to do this when the original value is no longer needed”). Since the derived context fully replaces the parent, keeping the same name makes that intent clear.

Nonetheless, I don't have a strong opinion. I can name it differently if that feels clearer or easier to follow.