In the light of the recent discussion upstream, it looks quite clear that the test failures are due to the lack of SSE2 in Debian's i686 rust target (and resulting unsound floating point behavior). The failures themselves were triggered by your switch from dh-cargo to dh-rust, which caused autopkgtests to start using the release rather than the debug profile (it's easy to see the profile switch at https://ci.debian.net/packages/r/rust-wide/testing/i386/). The bugs, however, were always there.
The fact that I was seeing failures as early as v0.7.11-2 whereas Debian's CI was not is also easily explained: you set Architecture: all so the packages are built on amd64 in Debian's CI which always passes tests (including those in dh_auto_test), whereas I was building them on i386, which always fails them with the release profile. The latter is used in dh_auto_test by the fork of dh-cargo you embedded in rust-wide until v0.7.25-2, but not in autopkgtests which until then used mainline dh-cargo. Had I built the packages on amd64 and then only run autopkgtests - not the entire build - on i386, I'm pretty sure that would have shown tests first failing in v0.7.26-1 as in Debian's CI. Given that upstream has closed the bug as "can't fix" I guess there's not much left to do other than removing the package from i386.
