$ grep COMPRESS /etc/initramfs-tools/initramfs.conf
# COMPRESS: [ gzip | bzip2 | lz4 | lzma | lzop | xz | zstd ]
COMPRESS=gzip

$ file --mime-type /boot/initrd.img-`uname -r`
/boot/initrd.img-5.11.8+: application/gzip

$ ls -1sS --block-size=1 ./initrd.img-5.11.8+.*
183033856 ./initrd.img-5.11.8+.raw
 81076224 ./initrd.img-5.11.8+.lz4
 78315520 ./initrd.img-5.11.8+.lzop
 54329344 ./initrd.img-5.11.8+.gzip
 51761152 ./initrd.img-5.11.8+.zstd
 50081792 ./initrd.img-5.11.8+.bz2
 36548608 ./initrd.img-5.11.8+.xz
 36540416 ./initrd.img-5.11.8+.lzma

$ \time -f %e cat ./initrd.img-5.11.8+.raw > /dev/null
0.03
$ \time -f %e lz4cat ./initrd.img-5.11.8+.lz4 > /dev/null
0.38
$ \time -f %e lzop -d -c ./initrd.img-5.11.8+.lzop > /dev/null
0.42
$ \time -f %e zstdcat ./initrd.img-5.11.8+.zstd > /dev/null
0.44
$ \time -f %e zcat ./initrd.img-5.11.8+.gzip > /dev/null
1.38
$ \time -f %e lzma -d -c ./initrd.img-5.11.8+.lzma > /dev/null
3.22
$ \time -f %e xzcat ./initrd.img-5.11.8+.xz > /dev/null
3.37
$ \time -f %e bzcat ./initrd.img-5.11.8+.bz2 > /dev/null
9.39

$ sudo git -C /etc diff HEAD /etc/initramfs-tools/initramfs.conf
diff --git a/initramfs-tools/initramfs.conf b/initramfs-tools/initramfs.conf
index 01bdd85..a0c051b 100644
--- a/initramfs-tools/initramfs.conf
+++ b/initramfs-tools/initramfs.conf
@@ -41,7 +41,7 @@ KEYMAP=n
 # COMPRESS: [ gzip | bzip2 | lz4 | lzma | lzop | xz | zstd ]
 #

-COMPRESS=gzip
+COMPRESS=zstd

 #
 # DEVICE: ...

$ update-initramfs -h

Usage: update-initramfs {-c|-d|-u} [-k version] [-v] [-b directory]

Options:
 -k version     Specify kernel version or 'all'
 -c             Create a new initramfs
 -u             Update an existing initramfs
 -d             Remove an existing initramfs
 -b directory   Set alternate boot directory
 -v             Be verbose

See update-initramfs(8) for further details.

$ sudo update-initramfs -k `uname -r` -u -v

$ ls -s --block-size=1 /boot/initrd.img-5.11.8+
54542336 /boot/initrd.img-5.11.8+
$ ls -s --block-size=1 /boot/initrd.img-5.11.8+
41611264 /boot/initrd.img-5.11.8+
$ file --mime-type /boot/initrd.img-5.11.8+
/boot/initrd.img-5.11.8+: application/zstd
$ zstd -lv /boot/initrd.img-5.11.8+
*** zstd command line interface 64-bits v1.4.8, by Yann Collet ***
/boot/initrd.img-5.11.8+
# Zstandard Frames: 1
Window Size: 8.00 MB (8388608 B)
Compressed Size: 39.53 MB (41446437 B)
Decompressed Size: 174.55 MB (183032320 B)
Ratio: 4.4161
Check: XXH64

$ grep zstd /usr/sbin/mkinitramfs
zstd)   compress="zstd -q -19 -T0" ;;

$ \time -f%e zstdcat -T1 /boot/initrd.img-5.11.8+ > /dev/null
0.50

case "${compress}" in
gzip)   # If we're doing a reproducible build, use gzip -n
        if [ -n "${SOURCE_DATE_EPOCH}" ]; then
                compress="gzip -n"
        # Otherwise, substitute pigz if it's available
        elif command -v pigz >/dev/null; then
                compress=pigz
        fi
        ;;
lz4)    compress="lz4 -9 -l" ;;
zstd)   compress="zstd -q -19 -T0" ;;
xz)     compress="xz --check=crc32"
        # If we're not doing a reproducible build, enable multithreading
        test -z "${SOURCE_DATE_EPOCH}" && compress="$compress --threads=0"
        ;;
bzip2|lzma|lzop)
        # no parameters needed
        ;;
*)      echo "W: Unknown compression command ${compress}" >&2 ;;
esac

$ count=1;while [[ $count -lt 19 ]];do zstdcat /boot/initrd.img-5.11.8+ | zstd -T0 -$count -c - > /tmp/zstd-$count.zstd;count=$(( $count+1 ));done
$ ls -1sS --block-size=1 /tmp/zstd-*
56188928 /tmp/zstd-1.zstd
53272576 /tmp/zstd-2.zstd
51761152 /tmp/zstd-3.zstd
51466240 /tmp/zstd-4.zstd
50061312 /tmp/zstd-5.zstd
49614848 /tmp/zstd-6.zstd
47431680 /tmp/zstd-7.zstd
46690304 /tmp/zstd-8.zstd
46424064 /tmp/zstd-9.zstd
45973504 /tmp/zstd-10.zstd
45850624 /tmp/zstd-11.zstd
45686784 /tmp/zstd-12.zstd
45539328 /tmp/zstd-13.zstd
45371392 /tmp/zstd-14.zstd
45309952 /tmp/zstd-15.zstd
44093440 /tmp/zstd-16.zstd
42987520 /tmp/zstd-17.zstd
41705472 /tmp/zstd-18.zstd
41447424 /tmp/zstd-19.zstd
$ ls -1S /tmp/zstd-* | xargs -I{} -n1 sh -c "echo -n \"{} \"; \time -f%e zstdcat -T0 {} > /dev/null"
/tmp/zstd-1.zstd 0.37
/tmp/zstd-2.zstd 0.36
/tmp/zstd-3.zstd 0.40
/tmp/zstd-4.zstd 0.47
/tmp/zstd-5.zstd 0.44
/tmp/zstd-6.zstd 0.42
/tmp/zstd-7.zstd 0.40
/tmp/zstd-8.zstd 0.37
/tmp/zstd-9.zstd 0.35
/tmp/zstd-10.zstd 0.40
/tmp/zstd-11.zstd 0.41
/tmp/zstd-12.zstd 0.38
/tmp/zstd-13.zstd 0.39
/tmp/zstd-14.zstd 0.39
/tmp/zstd-15.zstd 0.43
/tmp/zstd-16.zstd 0.37
/tmp/zstd-17.zstd 0.42
/tmp/zstd-18.zstd 0.53
/tmp/zstd-19.zstd 0.68

$ wget https://cdn.kernel.org/pub/linux/kernel/v5.x/incr/patch-5.11.8-9.xz
$ cd linux-5.11
$ xzcat ../patch-5.11.8-9.xz | patch -p1
$ grep ^COMPRESS= /etc/initramfs-tools/initramfs.conf
COMPRESS=zstd
$ time make -j`nproc` bindeb-pkg
$ ls -1sS ../*5.11.9*
737300 ../linux-image-5.11.9+-dbg_5.11.9+-5_amd64.deb
 59584 ../linux-image-5.11.9+_5.11.9+-5_amd64.deb
  8040 ../linux-headers-5.11.9+_5.11.9+-5_amd64.deb
  1124 ../linux-libc-dev_5.11.9+-5_amd64.deb
     8 ../linux-5.11.9+_5.11.9+-5_amd64.buildinfo
     4 ../linux-5.11.9+_5.11.9+-5_amd64.changes
$ sudo apt install ../linux-image-5.11.9+_5.11.9+-5_amd64.deb ../linux-headers-5.11.9+_5.11.9+-5_amd64.deb ../linux
-libc-dev_5.11.9+-5_amd64.deb
$ file /boot/initrd.img-5.11.9+
/boot/initrd.img-5.11.9+: Zstandard compressed data (v0.8+), Dictionary ID: None
$ ls --block-size=1 -s /boot/initrd.img-5.11.9+
41602048 /boot/initrd.img-5.11.9+
$ sudo shutdown -r now 'kernel upgrade'

$ dpkg-query -W initramfs-tools-core zstd
initramfs-tools-core    0.140
zstd    1.4.8+dfsg-2.1
$ lsb_release -dr
Description:    Debian GNU/Linux bullseye/sid
Release:        unstable
$ uname -srm
Linux 5.11.9+ x86_64