Bungie has acknowledged the issue and has provided an update to everyone. Here's what they have to say regarding the problem.
Destiny 2 The Witch Queen is not pre-loading on PS4

Bungie has announced that some players are unable to pre-load the PS4 required content as it is not available to download for them due to an issue on their end. However, they should be able to do so at 9 AM PST on 22nd February after Update 4.0.0.1 becomes available.
Due to an unforeseen issue, PS4 Required Content is not yet available for download. Players using the PS4 version of Destiny 2 can download these files at 9 AM PST tomorrow when Update 4.0.0.1 becomes available.
— Bungie Help (@BungieHelp) February 22, 2022
All Required Content is ~72 GB total.
Stay tuned for updates.
The size of the content is approximately 72 GB and players are not happy and they are asking for compensation.
We are owed a better explanation than this every other platform gets early download and access to game at launch. I get to wait 8 or 9 hours to even get a chance at access. This is totally unacceptable and we deserve compensation. You lied to ps4 players fix it.
— Michael Linderson (@BoyLazlo) February 22, 2022
Destiny 2: The Witch Queen expansion will be bringing new weapons, campaign, new destinations, a reworked Void subclass, and more to the game. As of now, the game servers are under maintenance and players who try to log in to Destiny 2 will be put in queues until it ends.
If you still face issues while downloading the Destiny 2: The Witch Queen update on PS4 after it releases, you can report it on Bungie help center.
You can have a look at the reveal trailer of Destiny: The Witch Queen below.
Make sure to check out our dedicated Destiny 2 section to stay updated with the latest news, guides, and more regarding the game.
Featured image courtesy of Bungie.