You could try out some freeware like https://codebox.net/pages/bitmeteros
I haven't used it, but seems to offer exactly what you're looking for.
"BitMeter OS is a free, open-source, bandwidth monitor that works on Windows, Linux and Mac OSX. BitMeter OS keeps track of how much you use your internet/network connection, and allows you to view this information either via a web browser, or by using the command line tools."
I use Bit Meter OS throughout the house on all of my family's devices so I can easily see who's computer is dragging down the internet. I believe that it would also work well for data tracking. It has a great web interface and is always logging with very little background usage. Highly recommend!
This has to be done on the router, some of them have features to track bandwidth usage.
If yours does not, you can install an internet bandwidth monitoring application e.g. BitMeter ( https://codebox.net/pages/bitmeteros) on each computer and track it that way. This will give you readings of how much each of those individual computers are using. This won't help if you have tablets / phones / smart TVs / etc. that use a lot of data, but if most of your data usage is coming from people on those computers then you can monitor it that way.
Android phones also have a section for tracking Wi-Fi data usage, so if you have a few problem devices you can find out why they used so much data on those screens.
The simple way to check would be to take every other device off the network and then try the PS4. If the PS4 is still having issues, then the problem is either with the PS4 itself or the network that it's trying to connect to.
You can also try running a bandwidth monitor to like BitMeter OS (free and open source) or NetWorx (free).