Monitoring software and ostriage are two seperate things. Monitoring software checks your device in real time and feeds things like screenshots back to the PPU, so if you typed in one of their watchwords, it would grab a screenshot of what you were doing at the time. It is very intrusive, because it is running in the background all the time. I offered to let them install it on my device but they said they only have a small number of licences, so they weren't going to bother.
Ostriage is basically taking a snapshot of what is on your device, at the time the PPU visit you. Sometimes they just do a manual check of my browsing history, but other times they insert a USB stick, which runs the ostriage software. As far as privacy is concerned, it probably comes under the very broad definition of checking or inspecting your devices, which is allowed by the SHPO.
It's intended for digital forensic investigators to use, when they arrest somebody and seize their devices. The idea is to let them inspect the device for anything naughty, on the spot, rather than having to take it to a lab. The main focus is images (obviously), and certain keywords, but it hoovers up lots of other stuff which might be useful for an investigation. How much use it is to the PPU depends on their level of IT knowledge. Mine is only really interested in the images.
But by playing around with tools like osforensics, I was able to see what they see. It can be a real eye opener, to find out just how much data they can extract.