It is heavily not recommended to try to hide the default “post” CPT from WordPress, since many plugins are manipulating their posts, meaning that they won’t care about WP Customer Area restrictions.
The Protect Post Types add-on is made to make all contents private from a given CPT, and add assignments boxes to them, which could allow to create a new section into your private area, but this is absolutely not recommended with the “post” default WordPress CPT.
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