Human cognitive biases in software engineering can lead to costly errors. While general-purpose AI (GPAI) systems may help mitigate these biases due to their non-human nature, their training on human-generated data raises a critical question: Do GPAI systems themselves exhibit cognitive biases? To investigate this, we present the first dynamic benchmarking framework to evaluate data-induced cognitive biases in GPAI within software engineering workflows. Starting with a seed set of 16 hand-crafted realistic tasks, each featuring one of 8 cognitive biases (e.g., anchoring, framing) and corresponding unbiased variants, we test whether bias-inducing linguistic cues unrelated to task logic can lead GPAI systems from correct to incorrect conclusions. To scale the benchmark and ensure realism, we develop an on-demand augmentation pipeline relying on GPAI systems to generate task variants that preserve bias-inducing cues while varying surface details. This pipeline ensures correctness (88-99% on average, according to human evaluation), promotes diversity, and controls reasoning complexity by leveraging Prolog-based reasoning. We evaluate leading GPAI systems (GPT, LLaMA, DeepSeek) and find a consistent tendency to rely on shallow linguistic heuristics over more complex reasoning. All systems exhibit bias sensitivity (6-35%), which increases with task complexity (up to 49%) and highlights risks in AI-driven software engineering.