Was it an older teacher/teaching assistant? I don't mean to be ageist, but I think it may be relevant in that I am in my 50s and that is the kind of outburst that I recall happened sometimes with teachers in my state schools in a working class area back in the 1980s. Sometimes children could be very cheeky, perhaps showing off, or emulating behaviour of older siblings, or just not yet having learned to read the room and pick their moment. And then, on a bad day, a teacher would lose control of themselves and yell and shout disproportionately at the offender. I can still remember specific ( kind of traumatic) incidents, and where we were all sat and how it felt observing it, and I was not even the target of the teacher's fury. When we discuss these incidents among old schoolfriends, others are often astonished that it was a fairly regular, if not frequent, part of school life.
Teacher training is very different now, and I would expect teachers to know that expectations on them are very different than in the past, regardless of the prevailing attitudes in their current school. In the very strict academy schools now, children seem to receive sanctions very quickly bu,t if anything, there is a tendency to over-control teachers as well as kids. Losing it and yelling isn't something that most schools would find acceptable in a teacher.
I wonder if an overwhelmed teacher has reacted in a manner that they experienced at some time in the past, maybe in school. Any or all of what I have suggested could be entirely irrelevant, but somewhere along the line they have learned to respond to stress by reacting loudly in the moment, rather than pausing and dealing with things in a sensible, moderate way.
I feel very sorry for your child because the response was disproportionate and distressingly unhelpful, even if we take the most uncharitable possible interpretation of your child's own part in it. 6 year olds are capable of being utterly infuriating, but for a single incident involving a single child (assuming there aren't underlying problems or an escalation of previous behaviour) then some time for both parties to cool down, and a clear (stern if appropriate) chat about expectations, should be enough to turn things around IMO.
The fact that the incident began with 6yo children being told, in such a harsh way, to be silent, and then for it to erupt like that, would be a real cause of concern for me, and I'd want to discuss the teacher's behaviour and the effects on the child, with a senior membr of staff in a private appointment. If the school thinks your child was at fault, you should be receptive to that too, but the two things need separate attention and you are not unreasonable to be concerned. The teacher may need and benefit from help, and/or they may need to be sanctioned, and that's something the school leaders need to be concerned with.