Upgrading other systems for comparison so far also showed no problems with this.
Nor with file ownership (as asked on askubuntu).

Focal:
ubuntu@ubuntu:~$ sudo ls -laF /run/chrony*
-rw-r--r-- 1 root    root     5 Feb  2 07:23 /run/chronyd.pid
/run/chrony:
total 0
drwxr-x---  2 _chrony _chrony   60 Feb  2 07:44 ./
drwxr-xr-x 33 root    root    1040 Feb  2 07:59 ../
srwxr-xr-x  1 _chrony _chrony    0 Feb  2 07:23 chronyd.sock=

Jammy after upgrade:
ubuntu@ubuntu:~$ sudo ls -laF /run/chrony*
/run/chrony:
total 4
drwxr-x---  2 _chrony _chrony   80 Feb  2 08:25 ./
drwxr-xr-x 34 root    root    1060 Feb  2 08:30 ../
-rw-r--r--  1 root    root       6 Feb  2 08:25 chronyd.pid
srwxr-xr-x  1 _chrony _chrony    0 Feb  2 08:25 chronyd.sock=


No change of permissions and no issue (here for me at least)


This is all that came by on do-release-upgrade
ubuntu@ubuntu:~$ journalctl -f | grep chrony
Feb 02 08:01:52 ubuntu sudo[24901]:   ubuntu : TTY=pts/3 ; PWD=/home/ubuntu ; USER=root ; COMMAND=/usr/bin/ls -laF /run/chrony /run/chronyd.pid

Feb 02 08:23:27 ubuntu audit[41288]: AVC apparmor="STATUS" operation="profile_replace" profile="unconfined" name="/usr/sbin/chronyd" pid=41288 comm="apparmor_parser"
Feb 02 08:23:27 ubuntu kernel: audit: type=1400 audit(1675326207.963:57): apparmor="STATUS" operation="profile_replace" profile="unconfined" name="/usr/sbin/chronyd" pid=41288 comm="apparmor_parser"
Feb 02 08:25:54 ubuntu audit[47223]: AVC apparmor="STATUS" operation="profile_replace" profile="unconfined" name="/usr/sbin/chronyd" pid=47223 comm="apparmor_parser"
Feb 02 08:25:54 ubuntu kernel: audit: type=1400 audit(1675326354.637:65): apparmor="STATUS" operation="profile_replace" profile="unconfined" name="/usr/sbin/chronyd" pid=47223 comm="apparmor_parser"
Feb 02 08:25:57 ubuntu chronyd[7147]: chronyd exiting
Feb 02 08:25:57 ubuntu systemd[1]: Stopping chrony, an NTP client/server...
Feb 02 08:25:57 ubuntu systemd[1]: chrony.service: Deactivated successfully.
Feb 02 08:25:57 ubuntu systemd[1]: Stopped chrony, an NTP client/server.
Feb 02 08:25:57 ubuntu systemd[1]: Starting chrony, an NTP client/server...
Feb 02 08:25:57 ubuntu chronyd[47310]: chronyd version 4.2 starting (+CMDMON +NTP +REFCLOCK +RTC +PRIVDROP +SCFILTER +SIGND +ASYNCDNS +NTS +SECHASH +IPV6 -DEBUG)
Feb 02 08:25:57 ubuntu chronyd[47310]: Frequency 13.180 +/- 0.224 ppm read from /var/lib/chrony/chrony.drift
Feb 02 08:25:57 ubuntu chronyd[47310]: Using right/UTC timezone to obtain leap second data
Feb 02 08:25:57 ubuntu chronyd[47310]: Loaded seccomp filter (level 1)
Feb 02 08:25:57 ubuntu systemd[1]: Started chrony, an NTP client/server.
Feb 02 08:26:04 ubuntu chronyd[47310]: Selected source 194.36.144.87 (0.ubuntu.pool.ntp.org)
Feb 02 08:26:04 ubuntu chronyd[47310]: System clock TAI offset set to 37 seconds
Feb 02 08:27:10 ubuntu chronyd[47310]: Selected source 185.125.190.56 (ntp.ubuntu.com)


And it is working fine after upgrade
ubuntu@ubuntu:~$ systemctl status chrony
● chrony.service - chrony, an NTP client/server
     Loaded: loaded (/lib/systemd/system/chrony.service; enabled; vendor preset: enabled)
     Active: active (running) since Thu 2023-02-02 08:25:57 UTC; 5min ago
       Docs: man:chronyd(8)
             man:chronyc(1)
             man:chrony.conf(5)
   Main PID: 47310 (chronyd)
      Tasks: 2 (limit: 4433)
     CGroup: /system.slice/chrony.service
             ├─47310 /usr/sbin/chronyd -F 1
             └─47311 /usr/sbin/chronyd -F 1

Feb 02 08:25:57 ubuntu systemd[1]: Starting chrony, an NTP client/server...
Feb 02 08:25:57 ubuntu chronyd[47310]: chronyd version 4.2 starting (+CMDMON +NTP +REFCLOCK +RTC +PRIVDROP +SCFILTER +SIGND +ASYNCDNS +NTS +SECHASH +IPV6 -DEBUG)
Feb 02 08:25:57 ubuntu chronyd[47310]: Frequency 13.180 +/- 0.224 ppm read from /var/lib/chrony/chrony.drift
Feb 02 08:25:57 ubuntu chronyd[47310]: Using right/UTC timezone to obtain leap second data
Feb 02 08:25:57 ubuntu chronyd[47310]: Loaded seccomp filter (level 1)
Feb 02 08:25:57 ubuntu systemd[1]: Started chrony, an NTP client/server.
Feb 02 08:26:04 ubuntu chronyd[47310]: Selected source 194.36.144.87 (0.ubuntu.pool.ntp.org)
Feb 02 08:26:04 ubuntu chronyd[47310]: System clock TAI offset set to 37 seconds
Feb 02 08:27:10 ubuntu chronyd[47310]: Selected source 185.125.190.56 (ntp.ubuntu.com)