Only left-wing media outlets say he identified his wife, child, etc.

You claim that the Vancouver Sun is "left wing"?

What's your basis for that claim?

and only right-wing media outlets say he was jailed just for pronoun usage.

Mass resisitance, breitbard and the federalist?

It's a bit of a stretch to lump them in with media outlets isn't it? Surely we shouldn't be comparing the fake news industry with journalism?

but I only found evidence of him violating the pronoun mandate.

He didn't give the interviews reported on by the vancouver sun?

Furthermore, the left-wing media outlets never provide sources for their claims; I can't just trust them without evidence.

Jesus mate. You just linked to fucking breitbart.

It's hard to find the original videos, since they're banned from big tech for "hate speech," so all I have to work with is one clip I found on YouTube (that probably won't be there for long). There are longer interviews somewhere, but I didn't find them.

Okay. Most plausibly he did both. Gave an interview in which he misgendered his child. To be fair it wouldn't be know to the court if he misgendered his child in private, so that he breached that part of the court order implies that he breached the bit about talking publicly about it.

Even if he broke that part of the order too: it doesn't warrant six months in literal prison, unless he or someone else was sending them death threats —

If the court tells you to do something, and you don't, the punishment has to ramp up pretty quickly. If you keep asking people to comply, it wastes the court's time, and makes a mockery of the legal system if ignoring it is a viable option. You can be jailed indefinitely for contempt in the US. All you have to do to avoid literal prison is do what the judge says while you appeal.