Can I schedule a daily shutdown?

Most days I forget to shutdown and therefor don’t get the updates.

Is it possible to create a custom systemd timer to shut down at a specified time each day?

Is there another built in tool for running scheduled tasks?

What system are you running? If you are running a KDE system, then it does have a task scheduler in the settings. Where you can enter a command and specify to run at a given time every day. Though this uses cron jobs instead of systemd timers as far as I am aware.

You can also just create a manual systemd timer or cronjob (the latter is easier in my opinion) to do so.

For example, I have an example cronjob that will shut down the system at 9pm everyday
0 21 * * * shutdown now

This systemd timer should also do the same thing.

[Unit]
Description=Shutdown timer

[Timer]
OnCalendar=Daily
Hour=21

[Action]
ExecStart=/sbin/shutdown now

[Install]
WantedBy=multi-user.target