Spack doesn't support cross-compilation, so I don't think we should imply with docs that it can.

so, to chime in: Spack supports cross-compilation (to an extent);
and has been supporting this for a while;
( by cross-compilation i mean cross-architecture compilation )

firstly: there's a flag (called host_compatible ; seems to have been added here #29835) which seems to be enabled by default;
this disallows any target that is incompatible with the host;
so, just configuring a compiler like mentioned here (in the docs), is insufficient; the host_compatible flag will stop the build early;

back in 2019 there were 2 discussions (this one about trying to cross-compile boost and this one about trying to cross compile a GCC compiler)

we're also interested in this use-case;
so, i've tested cross-compilation of a few packages, and some work; other don't work
particularly the ones that need host-compilers to build some build-time tools;

i've found this issue (#17239) that starts to tackle this into a direction;
i'll maybe continue there;