How to determine the amount of app space available?
It's your /data partition running low on free space (as always when this error occurs – see our insufficient-memory tag-wiki for details, first-aid and further information). According to the output you've provided, only 700 MB out of 10 GB are available. The "storage low" error is triggered when free space here reaches 10%.

This limitation was introduced to keep a "safety margin" for the system. So the user gets a warning when it was exceeded. In this state, of course Google Play Store refuses to install any new app, as it considers the system alreading running "low on space" and doesn't want to "worsen the situation".



When the 10% rule was introduced, devices came with much less internal storage, so it was quite reasonable (think of those devices with less than 512 MB). Nowadays, it does no longer seem a good idea – especially with MTP being introduced to have the "internal storage" and "internal SD card" on one partition, spanning multiple Gigabytes. Looks like this is an issue not yet addressed or "simply forgotten".