It depends. The base model, sure you can't really figure out what percentage of it came from which data source since there's just too many data sources and that information is lost along the way. They're likely not using the entirety of SO to generate answers though. Retraining LLMs is ungodly expensive, so they can't retrain it every time a new Q or A is created, and even retraining on a regular basis would be impractical.

Instead, without knowing exactly how they're doing it of course, my guess is they're pulling relevant Q&As from their database, then using those results to improve the response (for example by providing them as context). If you're interested, look into retrieval-augmented generation.