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> There is a typo in https://www.lua.org/manual/5.3/manual.html .
> The source code defines luaL_openlib but the reference says it's
> luaL_openlibs .

Both luaL_openlib and luaL_openlibs exist in the code:

https://www.lua.org/source/5.3/lauxlib.c.html#luaL_openlib
https://www.lua.org/source/5.3/linit.c.html#luaL_openlibs

However, luaL_openlib is only present when LUA_COMPAT_MODULE is defined.