Hi, I've ran into the same or very similar issue of a GPU hang on a Debian system with an integrated Intel GPU, both Firefox and Chrome, and after some searching I found that it is likely caused by a driver bug in the Mesa driver for Intel graphics. See this thread:
https://gitlab.freedesktop.org/mesa/mesa/-/issues/11429
There is also a workaround mentioned in that thread, adding the line INTEL_DEBUG=reemit into /etc/environment should help, but will likely also have some negative effect on performance.