When I apply transparent background to QLineEdit and also apply QGraphicsDropShadowEffect, makes the caret disappears:
 

How to reproduce:

auto lineEdit = new QLineEdit(this); 
lineEdit->setStyleSheet("background-color: rgba(0, 0, 0, 155); color: white;"); 
lineEdit->setGeometry(100, 30, 200, 80); 

QGraphicsDropShadowEffect * eff = new QGraphicsDropShadowEffect();   
eff->setBlurRadius(20);    
eff->setOffset(0);     
eff->setColor(0xb2003b);    
lineEdit->setGraphicsEffect(eff);

Some things I noted:

Changing the background-color to 0, 0, 0, 255 and applying the shadow effect the caret returns.

As soon I drop the alpha to 240- the caret disappears.

Selecting the text from right to left the caret also returns, but very bugged like seen in the gif.