How do I uninstall the Royal Pack?

To delete (and re-download) the Royal Edition DLC, you should be able to do it as outlined here.

1. From the PS4™ Home screen, go to [Library] > [Purchased], and click on the game title.

2. Highlight the game or digital content you want to delete, press the OPTIONS button to open the menu. Select [Delete]. Only the downloadable content will be deleted, not the saved game data.

3. To re-download the game and add-ons, go to [Library] > [Purchased], and then select [Download] to reinstall your game. To make sure you have all the add-ons, highlight and select the [PlayStation Store] to find and download any additional content.

4. Click [Download].

I will say though that your reasoning to delete the Royal Edition doesn't seem like the best approach on waiting to face Omega until you're ready. Since the Omega can only be found Insomnia Ruins, which is exclusive to the Royal Edition DLC, uninstalling it would remove complete access to this area - not just Omega.

Additional, since your save file has been played with the Royal Edition DLC content, you may be unable to play on that save file until you re-install the DLC.^{Citation needed}

If your desire is to simply not face Omega, then the better options are:

• Staying away from Insomnia Ruins, or
• Staying away from the Omega spawn point
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If your goal is only to avoid getting steamrolled by Omega, then you don't need to uninstall the pack. Omega is not agressive, you can stand between its legs and take selfies without it attacking you: