Two additional commands I regularly use as a Sysadmin are
systemctl status without any unit to list show the general system status (lists units that are running, units that are starting and failed units right at the top)
And then
systemctl list-units --failed
To show me just the failed units and did deeper what the problem is.
On a properly set up system I should quickly be able to ascertain if everything is "up and running" just by systemds status