I must apologize for not mentioning the Rogowski coil for AC current measurement. I have never had the opportunity to use one, so there is not much that I can add.
For completeness, I guess I should mention the rotating disc that used to be on all power meters. For the life of me I can't remember that name of the effect that produces the rotation and I don't know of any modern application that uses this approach.
Like the Maxim MAX4211 TI produces a (low side) current and voltage monitor with an SPI output, the LMP92064. Your processor will have to do the multiplication to get to power, but that's what processors are good for!
I believe TI has one or two others, but it will have to wait untll I get back to work on Monday.
Need more bandwidht than a hall sensor or 1-5 Mhz consider magneto resistive. Same techology used in many harddrive read heads. Works like a hall sensor in that they need a bias current to read the restance change typicly aranged in a bridge. Due to the fast response time you can pulse the current to save power. Use two in oposition to cancel stray magnetic fields. Note they can be magntized by large fields most have a reset winding. Made by a number of outfits. Have fun.
Used a MR sensor a decade ago in a compass chip , absolutely awful for anything analog, the scale factor, linearity and offset would change all the time, so needed to reset all the time .
One advantage of MR (for on/off applications), is that the magnetic field sensitivity is in the plane of the chip, where as hall effect is perpendicular to chip. More useful being oriented this way with SMD sensors for shaft encoders, or current sensors when placed over a conductor. In both these applications a hall sensor would read nominally zero as its aligned with the null in the field.