After updating libMesh and running git submodule update --recursive, I still hit configure: error: Unsupported Intel compiler detected.

Hmm... ok, I think I see the issue. In acsm_compiler_flags.m4, the actual shell command that we run to determine if it's the Intel C++ compiler:

          is_intel_icx="`($CXX -V 2>&1) | grep 'Intel(R)' | grep 'Compiler' | grep 'oneAPI'`"

and the shell command to determine the compiler version:

                  ACSM_GXX_VERSION_STRING="`($CXX -V 2>&1) | grep 'Version '`"

And then we check for supported numerical versions:

                  AS_CASE("$ACSM_GXX_VERSION_STRING",
                  [*25.*], [AC_MSG_RESULT(<<< C++ compiler is Intel(R) icx 25 >>>)
                            ACSM_GXX_VERSION=intel_icx_v25.x],
                  [*24.*], [AC_MSG_RESULT(<<< C++ compiler is Intel(R) icx 24 >>>)
                            ACSM_GXX_VERSION=intel_icx_v24.x],
                  [*23.*], [AC_MSG_RESULT(<<< C++ compiler is Intel(R) icx 23 >>>)
                            ACSM_GXX_VERSION=intel_icx_v23.x],
                  [*22.*], [AC_MSG_RESULT(<<< C++ compiler is Intel(R) icx 22 >>>)
                            ACSM_GXX_VERSION=intel_icx_v22.x],
                  [*21.*], [AC_MSG_RESULT(<<< C++ compiler is Intel(R) icx 21 >>>)
                            ACSM_GXX_VERSION=intel_icx_v21.x],

but your compiler reports its Version as "dev.x.0" which I guess is because it's a special compiler specific to Aurora. The reason that we need to determine the version of the compiler is because some flags we use only work with certain versions of the compiler.

I suppose what we could do in your case is add a new case like the ones above matching [*dev*] and then set ACSM_GXX_VERSION=intel_icx_dev. I think that would allow the required flags to be set correctly for the compiler, later on in acsm_compiler_flags.m4.

It would probably be easiest to implement/test this on the system itself, as it would require updates to the autoconf-submodule combined with running bootstrap/configure within libmesh itself to test the change. We have some instructions on how to edit m4 files, and set up your system to run bootstrap. Or it might be easier to have one of the MOOSE developers look into it for you.

Thanks for the pointers @jwpeterson! I'll give this a go and will report back once I get libMesh to build / run into other issues.