As to OP’s question, what always surprises me is how people think their misbehaviour is minor and not chat ban worthy, for stuff that is really not something one would say to a random stranger in the street. The mechanism of “internet anonymity” is really something not to be underestimated.
What is also observed often - especially in forum conversations like this one here - is that players believe (or claim) they have been chat banned unfairly, remembering some instance that was indeed minor, but then when we look at the cases, the picture looks quite different: We see the whole chat log, and thus can easily retrace why a player has received a certain punishment. And we will also share that info with players who ask, but of course only privately and not shared with the whole forum.
As to the process of reporting, I recommend having a look a this chart here:
Spoiler

Or in a more elaborate and complete form, that monster here: https://forum-en-cdn.warthunder.com/original/2X/4/42643213f1f6e9dd846bb4728eb52d7615d464e2.jpeg
As to trigger-happyness of GM’s, well, in all the years as GM and Senior GM that’s not something that I ever observed. Admittedly, cases where a GM makes a mistake do happen - contrary to popular belief we are human after all - but wrong chatbans really are very rare. We’re also constantly in exchange about these things, so our team is always on the same page about moderation.
What’s also very funny is how the community kind of has developped their own beliefs regarding which GM is “good” or “bad”: You will see here or in other platforms and media “that GM XY has been unfair yet again!!!”, then when one looks at the case you will see that a) that infamous GM wasn’t even involved at all, and b) the chat ban wasn’t unfair at all.
Or even the belief that a GM has singled a player out and tries to get him into trouble as much as he can. Here I have to disappoint you guys: We process literally thousands of reports every month, neither can we keep track of all of you, nor do we really care.
It’s just one of those things about perception and what people want to believe…
And of course if a players is doubtful about his or her chatban, drop us a PM and we’ll have a look and try to sort it out together.