Not able to initialize my PS4 for total system reinstall

"So from what you said it sounds like the PS4 can read the update file you’ve put on the USB (assuming it’s the full update one for re-initializing the PS4 and not just updating it) but after it attempt to reboot itself to perform an update it just gets stuck on Safe Mode instead of installing the update.

That is a big indicator of a bad hard drive in most cases. You can take out the hard drive and plug it into a desktop computer (before plugging it in make sure the computer is turned off) if you have one to check the health of the hard drive. You can alternatively plug the 2.5” PS4 hard drive into a portable 2.5” drive enclosure to check the health using the program explained below.

You can use a program called Hard Disk Sentinel which you can download here to check the health of the hard drive.

If it reports bad, weak sectors or data transfer errors or any other relevant health problems the hard drive needs to be replaced + PS4 - re-initialized with new hard drive to fix the problem."

Yeah you have a bad hard drive. So, you need replace your hard drive and then reinstall the system software on to it. Then, your PS4 will be able to start up normally.

You need to purchase a new hard drive for your PS4 because the one you currently have now is damaged. After you take out the old hard drive and insert the new hard drive, you need to install the latest system software onto a USB drive.

Try to install the whole software and put it on USB drive formatted as FAT32, be sure that the SSD or the HDD is FAT32 or exFAT file systems and it well work