https://bugs.debian.org/1114664 crossgrader alters
/usr/share/initramfs-tools/hook-functions
which belongs to
initramfs-tools-core

crossgrader_0.0.3+nmu5_all.deb
hook-functions is only referenced in
usr/lib/python3/dist-packages/debian_crossgrader/crossgrader.py
Looks like it intends to put the saved copy (saved to:
/usr/local/share/debian_crossgrader/hook-functions.bak
) of the original back when running --third_stage,
but it shouldn't change the file in the first place (policy, etc.),
and also looks like it also fails to revert.
If/as needed, it should probably add its own non-conflicting hook
elsewhere and clean that up with removal or purge.

summary of changes crossgrader makes to hook-functions (doesn't
include all changes, e.g. comments, empty lines):
-	local src target x nonoptlib ret
+# begin arch-check-hook
+check_file_arch () {
+    local arch_match arch_match_output
+    arch_match_output=$(python3 -c "import sys; from debian_crossgrader.utils.elf import e_machine; val=e_machine('${1}'); sys.exit(0 if val is None else val != e_machine('/usr/bin/dpkg'))")
+    arch_match=${?}
+    printf '%s' "${arch_match_output}" | sed 's/^/crossgrader initramfs hook: /'
+    if [ ${arch_match} -ne 0 ]; then
+        echo "crossgrader initramfs hook: (WARNING) initramfs binary ${1} might not be in the correct architecture."
+        echo 'crossgrader initramfs hook: Ensure that it can be executed or crossgrade the package containing it, then update the initramfs again.'
+        echo "crossgrader initramfs hook: output of \`file ${1}\`:"
+        file "${1}"
+    fi
+}
+check_file_arch "${1}"
+# end arch-check-hook

Most of what it changes (notably adds), is found here:
usr/lib/python3/dist-packages/debian_crossgrader/arch-check-hook.sh

Looks like
usr/lib/python3/dist-packages/debian_crossgrader/crossgrader.py
makes the changes to
/usr/share/initramfs-tools/hook-functions
Apparent intent is to augment copy_exec function

Looks like
/etc/initramfs-tools/hooks/
might be way to do the needed override in a policy compliant way