Function analyze_plan_with_context 

pub async fn analyze_plan_with_context(
    plan: Arc<dyn ExecutionPlan>,
    options: LanceExecutionOptions,
    task_context: Option<Arc<TaskContext>>,
) -> Result<String>

Analyze a plan, optionally under a caller-provided TaskContext.

When task_context is Some, the plan executes under it instead of the context derived from options. Callers whose nodes read session-config extensions at execution time (e.g. distributed routing identity) must pass the context carrying those extensions; otherwise the nodes error during execute and AnalyzeExec reports an empty, unexecuted plan tree instead of surfacing the error.