PlayStation 4 Pro downloads or updates very slowly

The checks in more detail

The internal 2.5 inch hard drive is slow, and a very full drive slows writing, so freeing space and rebuilding the database in Safe Mode helps, and an SSD swap makes installs faster. Set the DNS to a public server and check the router's firmware. Verify with another device that your line gives the speed you pay for. PlayStation's servers can be busy after a big release, so a slow download on launch day is not your fault; try later. Pause and resume the download or restart the console if it stalls at one percentage.

In rest mode the console can still download if the setting is enabled, and you can start a download and then put the console into rest mode: in Settings, Power Save Settings, Set Features Available in Rest Mode, tick Stay Connected to the Internet and Enable Turning On PS4 from Network, which lets updates and downloads continue when the screen is off. Large games on this console download as a single package plus patches, and the console checks the whole file when it finishes, so the last few percent can appear slow while it verifies.

Wait for the verification before assuming the download is stuck, and keep the console powered until the status says it is ready. If a download is very slow only on one game, check that the game's size matches what the store lists, because a patch can add many gigabytes, and use the Downloads list under Notifications to see the true size and time left.