HP Firmware Updater stalls (I am trying to update firmware to be able to print PDFs)

[PDFs_so_slow]

I have an HP LaserJetPro m402dw. It is about five years old. I use it on an iMac with o/s Big Sur. It is connected by USB. For at least the past two years my printer has been painfully slow at printing PDFs and will often only print 1-2 pages per job, even though the PDF may run to 20-100 pages. If I try to print more than 2 pages at a time the job just disappears after a short time in my printer queue. By looking at my printer (as opposed to my iMac screen) when I try to print more than two pages of a PDF at a time, I see a message saying something along the lines of: hp printer memory is low job canceled

I searched online to see what the problem was. One suggestion was that the printer firmware needs to be updated. This seemed promising as I have never updated the firmware and, having conducted a search on the HP website I identified that there is a firmware update for Mac (HP LaserJet Pro Series Mac Firmware Update Utility, version 20211118) dated 9 December 2021.

I downloaded this firmware update and opened it. On doing so I am then presented with "HP Firmware Updater". When I then attempted to open this I was initially met with a message saying something along the lines of: HP Firmware Updater cannot be opened because the developer cannot be verified.  I got around this by going into my Security and Privacy settings and allowing the firmware update to open.

However, when I did manage to open the HP Firmware Updater I encountered another problem and I have not been able to overcome this. The first phase of the HP Firmware Updater is "Device Discovery". My HP LaserJetPro m402dw should appear under "Device Name"  but instead nothing appears. There is an Apple activity indicator in the bottom right which spins indefinitely (1 hour+) with no progress, and a progress bar which is clearly stuck approximately half way. I have tried deleting it and downloading it again multiple times but on each occasion the outcome is the same. I do not know how to overcome the fact that the HP Firmware Updater has obviously stalled. 

There is a checkbox option in HP Firmware Updater under "Device Discovery" to "Add Device Manually", but the only options for "Address Type" are: "Host or Bonjour Domain Name", "IPv4" and "IPv6". None of these options seem to apply to my HP LaserJetPro m402dw because it is connected to my iMac by USB and is not accessed through a domain name or through a network.

After having encountered this difficulty earlier today I removed the  HP LaserJetPro m402dw from my device and reinstalled it using HP Install Easy Start (version 2.12.0.211012) dated 14 October 2021. However, the problem with HP Firmware Updater persists in exactly the same way as before, and any PDFs which are more than a couple of pages can still only be printed a couple of pages at a time.

For completeness, based on a Configuration Report my HP LaserJetPro m402dw has a total memory of 128mb and an available memory of 65.17mb.

I would be grateful for guidance as to how to resolve this persistent problem.

[Repairatrooper]

Try connecting via wired or wireless network. It is possible that updates are disabled on the printer itself and you will need access to the embedded web server of the printer to easily check and change that. You can check the menus on the control panel of the printer as well but some options are not available that way.