It doesn't take that long because of gravity, it's the path taken to the surface.

https://www.astronomy.com/science/i-heard-that-the-light-from-nuclear-fusion-reactions-in-the-suns-core-takes-about-200000-years-to-reach-its-surface-i-thought-the-speed-of-light-is-constant-why-does-it-take-so-long/

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You're absolutely right, I might have simplified it too much ("gravity" in quotes) though the fusion which causes the radiation is at last caused by the immense gravity.

But your shared link explains it better than I could. 👍🤗