[Help] with using old HDD in new PS4

In 2015 i upgraded my PS4’s hard drive to a new 2TB drive.

I have recently upgraded to a new PS4 and would like to use the 2TB hard drive, that i’ve been using, in the new PS4.

Simply installing the 2TB HDD, into the new PS4, doesn’t make it instantly work and comes up with -

Connect a USB storage device that contains an update file for reinstallation for version 4.72 or later.

You can download the update file for reinstallation from playstation.com

So, keep in mind that i have the USB that i used the first time around, when moving to the 2TB.
Am i, from this Playstation webpage, downloading the 350 or 900MB file to use on my USB in my PS4 and will using either of those downloads on my old HDD wipe it clean?/result in me losing all my capture gallery videos etc?

I realise that i can backup all my things from the Capture Gallery onto an external hard drive but since the old HDD is already installed in the new PS4 i’m trying to see what can be done with where i stand. Especially when i’d rather not have to remove the HDD from the new PS4 and install it in the old one again and buy an external Hard Drive case to back things up.

Realistically, i should have seen that it wouldn’t just instantly work as soon as i connected everything up.
Anyway, i’m here now asking questions, in hopefully the right place.

Basically, i want to continue using the same Hard Drive on a new PS4.

Any help on the matter would be greatly appreciated!