ASM: Search for full path even when using C or C++ compiler

When `CMAKE_{C,CXX}_COMPILER` is set but `CMAKE_ASM*_COMPILER` is
not, we copy the C or C++ compiler to use as the ASM compiler.
In this case we still need to search for the ASM compiler in case
the C or C++ compiler is not known as an absolute path.

Also do not copy the compiler id setting and let the normal detection
take place.  The C compiler id may not exist if the language has not
been enabled.

Fixes: #18406

Modules/CMakeDetermineASMCompiler.cmake

@@ -22,11 +22,9 @@ if(NOT CMAKE_ASM${ASM_DIALECT}_COMPILER)
   if("ASM${ASM_DIALECT}" STREQUAL "ASM") # the generic assembler support
     if(NOT CMAKE_ASM_COMPILER_INIT)
       if(CMAKE_C_COMPILER)
-        set(CMAKE_ASM_COMPILER "${CMAKE_C_COMPILER}" CACHE FILEPATH "The ASM compiler")
-        set(CMAKE_ASM_COMPILER_ID "${CMAKE_C_COMPILER_ID}")
+        set(CMAKE_ASM${ASM_DIALECT}_COMPILER_LIST ${CMAKE_C_COMPILER})
       elseif(CMAKE_CXX_COMPILER)
-        set(CMAKE_ASM_COMPILER "${CMAKE_CXX_COMPILER}" CACHE FILEPATH "The ASM compiler")
-        set(CMAKE_ASM_COMPILER_ID "${CMAKE_CXX_COMPILER_ID}")
+        set(CMAKE_ASM${ASM_DIALECT}_COMPILER_LIST ${CMAKE_CXX_COMPILER})
       else()
         # List all default C and CXX compilers
         set(CMAKE_ASM${ASM_DIALECT}_COMPILER_LIST