It sounds like a smart arse response, but I guess it could have been a genuine query, it depends on tone. I’d probably trust the teacher on that to an extent. You know your child. You know what they are prone to. I suspect you think it could have been a smart arse response otherwise you wouldn’t be wondering. If so, well - if it isn’t the consequences of his actions. He learned a boundary today.
In terms of disproportionate reactions, teachers are human too. If they are using that line, it’s because the class (or a student) has got on their last nerve. They effectively told him to shut up, and he spoke. If I’m already pissed off, I’d probably shout too. The nonsense about his friends comforting and him apologising was adding to the irritation, they just needed the class to STFU and he still wasn’t doing it. I’d have put him out of the class to calm down.
A 6 year old complaining they have to sit in silence is also very contextual. If he is naturally chatty, being told from time to time to be quiet will be sitting in silence. What’s probably happening is, he talks too much when he shouldn’t. No teacher of 6 year olds expects silence all the time.
Still crying at bedtime is an extreme reaction. I say this as a the parent of a highly strung kid, who when she was shouted at by a teacher in P4 (the first time ever, and it was for chatting when she shouldn’t) she cried about it when she told me for about 10 minutes. I told her she was doing well if this was the first time a teacher shouted at her and next time when she is told not to talk, don’t talk. There is rarely something that absolutely needs to be said in that moment. Just remind him he needs to not talk to his friends when they are supposed to be quiet, and if he does, he may get in trouble.
I wouldn’t bother the teacher about this. There isn’t going to be any outcome which will change anything. If the teacher is prone to shouting at the kids, they aren’t going to change. You could take it up the chain but on the strength of one report, nothing will happen. You don’t need them to tell you if he was being cheeky, you simply point out to him that even if it was genuine, it would always sound cheeky. He did not need to know that answer, but if he wanted to know, he could have waited and asked later, or asked you when he got home. He needs to learn to read the room.
Strict and scary teachers also varies from child to child. Mine loved the ones who were said to be strict and scary. They kept control, they didn’t allow kids to be disruptive, and according to her, if they chewed a kid out, the kid deserved it. Well behaved kids have nothing to fear from strict and scary teachers. If he is becoming anxious, what is he afraid of? Keep your powder dry, remind your child of the rules, but if it becomes a regular occurrence, bring it to them at that point.