WebAssembly (Wasm) is a binary instruction format that enables portable, sandboxed, and near-native execution across heterogeneous platforms, making it well-suited for serverless workflow execution on browsers, edge nodes, and cloud servers. However, its performance and stability depend heavily on factors such as startup overhead, runtime execution model (e.g., Ahead-of-Time (AOT) and Just-in-Time (JIT) compilation), and resource variability across deployment contexts. This paper evaluates a Wasm-based serverless workflow executed consistently from the browser to edge and cloud instances. The setup uses wasm32-wasi modules: in the browser, execution occurs within a web worker, while on Edge and Cloud, an HTTP shim streams frames to the Wasm runtime. We measure cold- and warm-start latency, per-step delays, workflow makespan, throughput, and CPU/memory utilization to capture the end-to-end behavior across environments. Results show that AOT compilation and instance warming substantially reduce startup latency. For workflows with small payloads, the browser achieves competitive performance owing to fully in-memory data exchanges. In contrast, as payloads grow, the workflow transitions into a compute- and memory-intensive phase where AOT execution on edge and cloud nodes distinctly surpasses browser performance.