Is this soldering iron and power supply combo grounded and if so, how?
If you use any regular ac/dc brick, it is not grounded.
You should not use the iron when it is not grounded.

Why you must ground it?
When you use a "floating" ac/dc brick, there will be charge or coupled AC current (typically half mains voltage) on the DC side of the transformer. Although small, it still has the capability of sparking any other circuitry to death. Just like ESD.

Even if a AC/DC brick has a three prong plug, this does not guarantee grounded DC side.

Explicitly ground the iron or DC side of the power supply yourself.

Many other soldering stations have a large mains transformer instead of a SMPS, this significantly reduces the leakage current to almost zero. You could use these when they are not grounded.