Hi there!
According to your issue, it does look like that the Hard drive is getting bad.
I recommend to replace this one first and see how that goes!
While you are there, maybe it's worth it to replace it for an SSD! Faster, less power consumption etc.
When replaced, you need to install the new PS4 software on it, which can be found here: https://www.playstation.com/en-us/support/hardware/ps4/system-software/
Make sure you get the ***"PS4 Console Reinstallation File". Not*** the update file.
Guide for how to replace the HDD: [guide|76790] It's really easy to do!
Please let us know how it goes!