Broken as in bin the SD Card and use another one, or broken in such a way that it would be worth trying a fresh install - if you are unsure, from your experience, if you were in this situation which option would you personally choose?
This is from when trying to install again:

[ INFO ] DietPi-Software | APT install for: xserver-xorg-core xserver-xorg-input -libinput xinit dbus-x11 xfonts-base x11-xserver-utils x11-utils libgl1-mesa-dri mesa-utils mesa-utils-extra xserver-xorg-video-fbdev, please wait...
E: dpkg was interrupted, you must manually run 'sudo dpkg --configure -a' to cor rect the problem.
[FAILED] DietPi-Software | APT install for: xserver-xorg-core xserver-xorg-input -libinput xinit dbus-x11 xfonts-base x11-xserver-utils x11-utils libgl1-mesa-dri mesa-utils mesa-utils-extra xserver-xorg-video-fbdev
- Command: apt-get -qq --allow-change-held-packages install xserver-xorg-core x server-xorg-input-libinput xinit dbus-x11 xfonts-base x11-xserver-utils x11-util s libgl1-mesa-dri mesa-utils mesa-utils-extra xserver-xorg-video-fbdev
[ INFO ] DietPi-Software | APT install for: xserver-xorg-core xserver-xorg-input -libinput xinit dbus-x11 xfonts-base x11-xserver-utils x11-utils libgl1-mesa-dri mesa-utils mesa-utils-extra xserver-xorg-video-fbdev, please wait...
E: dpkg was interrupted, you must manually run 'sudo dpkg --configure -a' to cor rect the problem.
[FAILED] DietPi-Software | APT install for: xserver-xorg-core xserver-xorg-input -libinput xinit dbus-x11 xfonts-base x11-xserver-utils x11-utils libgl1-mesa-dri mesa-utils mesa-utils-extra xserver-xorg-video-fbdev
- Command: apt-get -qq --allow-change-held-packages install xserver-xorg-core x server-xorg-input-libinput xinit dbus-x11 xfonts-base x11-xserver-utils x11-util s libgl1-mesa-dri mesa-utils mesa-utils-extra xserver-xorg-video-fbdev
[ INFO ] DietPi-Bugreport | cp /tmp/G_EXEC_ERROR_REPORT G_EXEC_ERROR_REPORT, ple ase wait...
[ OK ] DietPi-Bugreport | cp /tmp/G_EXEC_ERROR_REPORT G_EXEC_ERROR_REPORT
[ OK ] DietPi-Bugreport | Packing upload archive
[ OK ] DietPi-Bugreport | Sending bug report
[ INFO ] DietPi-Bugreport | Reference code: 7120d931-0a86-43cd-9a4d-fcca315d631f
#### Details:
- Date | Thu Jun 3 09:06:51 BST 2021
- Bug report | 7120d931-0a86-43cd-9a4d-fcca315d631f
- DietPi version | v7.2.3 (MichaIng/master)
- Image creator | DietPi Core Team
- Pre-image | Raspberry Pi OS (32-bit) Lite
- Hardware | RPi 3 Model B (armv7l) (ID=3)
- Kernel version | Linux DietPi 5.10.17-v7+ #1421 SMP Thu May 27 13:59:01 BST 20 21 armv7l GNU/Linux
- Distro | buster (ID=5,RASPBIAN=1)
- Command | apt-get -qq --allow-change-held-packages install xserver-xorg -core xserver-xorg-input-libinput xinit dbus-x11 xfonts-base x11-xserver-utils x 11-utils libgl1-mesa-dri mesa-utils mesa-utils-extra xserver-xorg-video-fbdev
- Exit code | 100
- Software title | DietPi-Software
#### Steps to reproduce:
<!-- Explain how to reproduce the issue -->
1. ...
2. ...
#### Expected behaviour:
<!-- What SHOULD happen? -->
- ...
#### Actual behaviour:
<!-- What IS happening? -->
- ...
#### Extra details:
<!-- Please post any extra details that might help solve the issue -->
- ...
#### Additional logs:
E: dpkg was interrupted, you must manually run ‘sudo dpkg --configure -a’ to cor rect the problem.
After sudo dpkg --configure -a I received errors and input the code you suggested:
dietpi@DietPi:~$ echo $PATH
/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/local/games:/usr/games
dietpi@DietPi:~$ command -v dmesg
/bin/dmesg
dietpi@DietPi:~$ [[ -f '/bin/dmesg' ]] && echo 'bash sees that file'
bash sees that file
dietpi@DietPi:~$ echo "$(</proc/mounts)"
/dev/root / ext4 rw,lazytime,noatime 0 0
devtmpfs /dev devtmpfs rw,relatime,size=465280k,nr_inodes=116320,mode=755 0 0
sysfs /sys sysfs rw,nosuid,nodev,noexec,relatime 0 0
proc /proc proc rw,nosuid,nodev,noexec,relatime 0 0
securityfs /sys/kernel/security securityfs rw,nosuid,nodev,noexec,relatime 0 0
tmpfs /dev/shm tmpfs rw,nosuid,nodev 0 0
devpts /dev/pts devpts rw,nosuid,noexec,relatime,gid=5,mode=620,ptmxmode=000 0 0
tmpfs /run tmpfs rw,nosuid,nodev,mode=755 0 0
tmpfs /run/lock tmpfs rw,nosuid,nodev,noexec,relatime,size=5120k 0 0
tmpfs /sys/fs/cgroup tmpfs ro,nosuid,nodev,noexec,mode=755 0 0
cgroup2 /sys/fs/cgroup/unified cgroup2 rw,nosuid,nodev,noexec,relatime,nsdelegate 0 0
cgroup /sys/fs/cgroup/systemd cgroup rw,nosuid,nodev,noexec,relatime,xattr,name=systemd 0 0
none /sys/fs/bpf bpf rw,nosuid,nodev,noexec,relatime,mode=700 0 0
cgroup /sys/fs/cgroup/cpu,cpuacct cgroup rw,nosuid,nodev,noexec,relatime,cpu,cpuacct 0 0
cgroup /sys/fs/cgroup/pids cgroup rw,nosuid,nodev,noexec,relatime,pids 0 0
cgroup /sys/fs/cgroup/freezer cgroup rw,nosuid,nodev,noexec,relatime,freezer 0 0
cgroup /sys/fs/cgroup/perf_event cgroup rw,nosuid,nodev,noexec,relatime,perf_event 0 0
cgroup /sys/fs/cgroup/devices cgroup rw,nosuid,nodev,noexec,relatime,devices 0 0
cgroup /sys/fs/cgroup/cpuset cgroup rw,nosuid,nodev,noexec,relatime,cpuset 0 0
cgroup /sys/fs/cgroup/blkio cgroup rw,nosuid,nodev,noexec,relatime,blkio 0 0
cgroup /sys/fs/cgroup/net_cls,net_prio cgroup rw,nosuid,nodev,noexec,relatime,net_cls,net_prio 0 0
systemd-1 /proc/sys/fs/binfmt_misc autofs rw,relatime,fd=27,pgrp=1,timeout=0,minproto=5,maxproto=5,direct 0 0
mqueue /dev/mqueue mqueue rw,relatime 0 0
debugfs /sys/kernel/debug debugfs rw,relatime 0 0
configfs /sys/kernel/config configfs rw,relatime 0 0
tmpfs /var/log tmpfs rw,lazytime,nosuid,nodev,noatime,size=51200k 0 0
tmpfs /tmp tmpfs rw,lazytime,nosuid,nodev,noatime,size=1048576k 0 0
/dev/mmcblk0p1 /boot vfat rw,lazytime,noatime,fmask=0022,dmask=0022,codepage=437,iocharset=ascii,shortname=mixed,errors=remount-ro 0 0
Please let me know if I can try anything else or provide any more information - or if I should go ahead and try a fresh install on the SD card, or scrap it for a new one.