refactor: DRY cycle request context handling

[somethingwithproof]

Problem

cycle.php repeats request-context extraction and default normalization logic in both cycle_graphs() and cycle().

Proposed change

• add a shared helper that builds/normalizes cycle request context
• use the helper in both rendering paths
• preserve behavior while reducing duplicated logic

Tests

• add standalone regression tests for helper behavior
• add assertions that both code paths use the shared helper
• run syntax checks on modified files