Limitations
Web browsers execute the WebAssembly (Wasm) bytecode in a sandboxed environment separated from the host. The sandboxed environment has some limitations, including
maximum of 4 GB because of the use of 32-bit indexes.
multithreading is still being standardized and implemented by browsers.
single instruction, multiple data (SIMD) is still being standardized and implemented by browsers.
can only escape the sandbox going through appropriate APIs.
Network
The biggest limitation for the end user is probably related with access to the internet that can happen using Fetch API or proxy.
Fetch API
The Wasm code uses the Fetch API directly and follows the same security of JavaScript running in the browser, for example Cross-Origin Resource Sharing (CORS).
Proxy
The Wasm code uses the Fetch API to contact a proxy server that is responsible to fulfill the access to the internet.
References
The State of WebAssembly – 2024 and 2025 by C. Gerard Gallant.
Making libcurl work in webassembly by Jeroen.
Making HTTP Requests with Pyodide by Nick George.