Hello,
This exact question was asked before in https://community.arm.com/support-forums/f/compilers-and-libraries-forum/53452/include-limits-h-on-arm-gnu-toolchain-11-3-rel1-x86_64-arm-none-eabi-is-this-a-bug. But as a summary, due to a bug, it is not possible to include arm-none-eabi/include/limits.h, as ./lib/gcc/arm-none-eabi/12.2.1/include-fixed/limits.h is prefered by the preprocessor. This is bad because lib/gcc/arm-none-eabi/12.2.1/include-fixed/limits.h is obviously not meant to be included directly, and arm-none-eabi/include/limits.h will even include it using include-next. The preprocessor will however search trough lib/gcc/arm-none-eabi/12.2.1/include-fixed before arm-none-eabi/include, so that the only fix is to change the toolchain by copying or moving arm-none-eabi/include/limits.h to lib/gcc/arm-none-eabi/12.2.1/include (works because that is the first path the preprocessor will check)
To me this is a problem because the code I am using checks for newlib, and arm-none-eabi/include/limits.h will pull in the correct defines/headers so that newlib is correctly recognized, while lib/gcc/arm-none-eabi/12.2.1/include-fixed/limits.h will not pull in those defines.
The linked post seems to already explain how to fix this issue. Other arm-none-eabi crosscompiler packages (such as the Arch Linux one, https://gitlab.archlinux.org/archlinux/packaging/packages/arm-none-eabi-gcc/-/blob/main/PKGBUILD) also dont suffer from this issue, so it seems to be a configuration issue on the side of ARM.