Don't fool around with this! Test it.
Seek out a grounded, GFCI-protected outlet (kitchen, bathroom) or RCD-protected outlet, preferably a 6 or 8 milliamp rated one.
Remove the cover plate from the outlet*, so you have access to the yoke (metal wings of the receptacle which take the mounting screws). This yoke should be tied to the Equipment Safety Ground,** which bypasses the GFCI. We need access to that.
Now, plug the soldering iron in, and touch it to the yoke repeatedly as it warms up. Don't hold it there, or you could melt the receptacle or plastic junction box.
When that's done, if it's possible to flip the plug over (looking at you Germany), flip the plug over and test again.
If it trips the GFCI, into the trash it goes
If the soldering iron is leaking current to the tip, it will trip the GFCI in about 10 milliseconds. That is an indication to throw it out, because it is internally leaking mains current onto the tip - which means it will leak mains current onto you. 10ma can kill. It can also stun you, and unconscious person + soldering iron is a bad combination.
If it is an expensive unit, you can maybe do a teardown to see if you can find dirt, splashed solder or frayed insulation that might be causing this.
What is the test testing? The GFCI detects by comparing current flow on hot and on neutral, to assure they are the same. If they are not, some current is taking a third path. So it detects all current flow that is not hot->neutral. We are using ground to create a third path for testing. We flip the plug over to exchange hot and neutral, because neutral->ground is harder to detect than hot->ground.
* As a low voltage DC electronics person, if you normally have a healthy fear of all things mains power, that is a good thing. And if you don't have that fear, obtain it. LVDC does nothing to prepare you for the hazards, rule-set and mind-set of mains power. But you can certainly do this.
** No relation to electronics GND/VSS/"common", that would be neutral. Equipment Safety Ground is a shield, but does not contact any mains conductor in any way (except for exactly one equipotential bond). As such, it entirely bypasses the GFCI - really, GFCIs don't use ground (except GFCI receptacles, to pass it through to appliances).