[k2] add fstat #2414

Job	Run time
focal / clang++ / c++17 / asan=off / ubsan=on	30m 32s
jammy / g++ / c++20 / asan=on / ubsan=off	28m 53s
focal / g++-10 / c++20 / asan=on / ubsan=off	32m 10s
	1h 31m 35s

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