Option to build without the standard library

🚀 The feature, motivation and pitch

ExecuTorch is intended for use in edge devices, even embedded systems. In these use cases it is required to reduce the size of the executable, and ExecuTorch are proud of the core library to be only few dozes of Kb. I think it will be very useful to be able compile without the standard CPP library.

The library already give a great flexibility for custom allocators, and I don't think there is some critical code that must have std.
From my attempt of compiling the lib without std I saw some use of std errors, clocks (which maybe I can override by providing another implementation for the platform/ headers), allocations in MemoryAllocator (maybe we can solve it with a cmake flag), and exceptions (rarely used, saw in some backends loading code).

I wrote Rust bindings for the library, and one of the features I would like to offer is exactly that, to compile without the std lib. In Rust you just add #![no_std] to the crate, in CPP you should do -nostdlib.

Alternatives

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Additional context

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RFC (Optional)

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cc @JacobSzwejbka @dbort @GregoryComer

Start by auditing the standard-library uses identified in the issue, including the platform/ headers, MemoryAllocator, CMake configuration, clocks, and exceptions in backend loading code. Map which components must change to support a no-standard-library build, then define a build and test path that verifies the core library compiles without the C++ standard library.