I have verified the fix on Jammy using systemd 249.11-0ubuntu3.10 from jammy-proposed:

nr@clean-jammy-amd64:~$ apt-cache policy systemd
systemd:
  Installed: 249.11-0ubuntu3.9
  Candidate: 249.11-0ubuntu3.10
  Version table:
     249.11-0ubuntu3.10 500
        500 http://archive.ubuntu.com/ubuntu jammy-proposed/main amd64 Packages
 *** 249.11-0ubuntu3.9 500
        500 http://archive.ubuntu.com/ubuntu jammy-updates/main amd64 Packages
        100 /var/lib/dpkg/status
     249.11-0ubuntu3.7 500
        500 http://security.ubuntu.com/ubuntu jammy-security/main amd64 Packages
     249.11-0ubuntu3 500
        500 http://archive.ubuntu.com/ubuntu jammy/main amd64 Packages
nr@clean-jammy-amd64:~$ cat /proc/cmdline 
BOOT_IMAGE=/boot/vmlinuz-5.19.0-45-generic root=UUID=32a6b55f-64d3-421b-a77d-2f9a2c6d68be ro quiet splash --- vt.handoff=7
nr@clean-jammy-amd64:~$ sudo apt install systemd -y
[sudo] password for nr: 
Reading package lists... Done
Building dependency tree... Done
Reading state information... Done
The following packages were automatically installed and are no longer required:
  libflashrom1 libftdi1-2 libllvm13 linux-headers-5.15.0-25
  linux-headers-5.15.0-25-generic linux-image-5.15.0-25-generic
  linux-modules-5.15.0-25-generic linux-modules-extra-5.15.0-25-generic
Use 'sudo apt autoremove' to remove them.
The following additional packages will be installed:
  libnss-systemd libpam-systemd libsystemd0 systemd-oomd systemd-sysv
  systemd-timesyncd
Suggested packages:
  systemd-container libtss2-rc0
The following packages will be upgraded:
  libnss-systemd libpam-systemd libsystemd0 systemd systemd-oomd systemd-sysv
  systemd-timesyncd
7 upgraded, 0 newly installed, 0 to remove and 217 not upgraded.
Need to get 5,312 kB of archives.
After this operation, 4,096 B disk space will be freed.
Get:1 http://archive.ubuntu.com/ubuntu jammy-proposed/main amd64 libnss-systemd amd64 249.11-0ubuntu3.10 [133 kB]
Get:2 http://archive.ubuntu.com/ubuntu jammy-proposed/main amd64 systemd-timesyncd amd64 249.11-0ubuntu3.10 [31.2 kB]
Get:3 http://archive.ubuntu.com/ubuntu jammy-proposed/main amd64 systemd-sysv amd64 249.11-0ubuntu3.10 [10.5 kB]
Get:4 http://archive.ubuntu.com/ubuntu jammy-proposed/main amd64 systemd-oomd amd64 249.11-0ubuntu3.10 [34.8 kB]
Get:5 http://archive.ubuntu.com/ubuntu jammy-proposed/main amd64 libpam-systemd amd64 249.11-0ubuntu3.10 [203 kB]
Get:6 http://archive.ubuntu.com/ubuntu jammy-proposed/main amd64 systemd amd64 249.11-0ubuntu3.10 [4,581 kB]
Get:7 http://archive.ubuntu.com/ubuntu jammy-proposed/main amd64 libsystemd0 amd64 249.11-0ubuntu3.10 [319 kB]
[...]
nr@clean-jammy-amd64:~$ apt-cache policy systemd
systemd:
  Installed: 249.11-0ubuntu3.10
  Candidate: 249.11-0ubuntu3.10
  Version table:
 *** 249.11-0ubuntu3.10 500
        500 http://archive.ubuntu.com/ubuntu jammy-proposed/main amd64 Packages
        100 /var/lib/dpkg/status
     249.11-0ubuntu3.9 500
        500 http://archive.ubuntu.com/ubuntu jammy-updates/main amd64 Packages
     249.11-0ubuntu3.7 500
        500 http://security.ubuntu.com/ubuntu jammy-security/main amd64 Packages
     249.11-0ubuntu3 500
        500 http://archive.ubuntu.com/ubuntu jammy/main amd64 Packages
nr@clean-jammy-amd64:~$ grep -Fsx systemd /run/reboot-required.pkgs
systemd
nr@clean-jammy-amd64:~$ reboot
[...]
nr@clean-jammy-amd64:~$ sudo systemctl daemon-reexec
nr@clean-jammy-amd64:~$ journalctl --grep "Found left-over process" -b 0
Aug 28 11:55:10 clean-jammy-amd64 systemd[1]: kerneloops.service: Found left-ov>
nr@clean-jammy-amd64:~$ cat /proc/1/cmdline | tr '\0' '\n'
/lib/systemd/systemd
--system
--deserialize
107
splash
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