I don't really like that
As I said - QTextEdit is not an HTML browser. It handles rich text and stores it as styled text blocks. It accepts subset of HTML as input but it does not store it as such. So it doesn't put the content in <p>. It simply has no notion of <p>, <div> etc. at all. That's the source of the remark in the docs, that the stylesheet is only applied on entry. After that there are no <div> to style. The output you get back is a result of another conversion, where every paragraph is simply output as <p>. It does not reflect what you input.
Take a look at the link I posted previously. QTextEdit supports only subset of HTML/CSS. It does not support class attribute or a "border" CSS property.
How about you try to operate directly on text blocks, and not go through HTML? Here's an example for a chat-like formatting:
QTextBlockFormat tbf1;
tbf1.setAlignment(Qt::AlignLeft);
tbf1.setBackground(Qt::red);
QTextBlockFormat tbf2;
tbf2.setAlignment(Qt::AlignRight);
tbf2.setBackground(Qt::green);
ui->textEdit->textCursor().beginEditBlock();
ui->textEdit->textCursor().setBlockFormat(tbf1);
ui->textEdit->textCursor().insertText("Wassup?\n");
ui->textEdit->textCursor().endEditBlock();
ui->textEdit->textCursor().beginEditBlock();
ui->textEdit->textCursor().setBlockFormat(tbf2);
ui->textEdit->textCursor().insertText("Nothin' much\n");
ui->textEdit->textCursor().insertText("Just playin' a game. How 'bout you?\n");
ui->textEdit->textCursor().endEditBlock();
ui->textEdit->textCursor().beginEditBlock();
ui->textEdit->textCursor().setBlockFormat(tbf1);
ui->textEdit->textCursor().insertText("Nothin' much\n");
ui->textEdit->textCursor().endEditBlock();
