Hmm, that is indeed the missing dependency module.
I’d recommend double checking and making sure your pf2e system version is at least 4.6.7, since that is another prerequisite for the module to show up. Considering that you’ve likely already run Punks in a Powderkeg which has the same prerequisites, it shouldn’t be that.
Copying your player character data to a new world is actually quite easy! You can make use of the Forge’s Shared Compendiums feature. This would allow you to copy your characters to a module, and then activate that module in the new world.
Another easy way to do it is to right click on the character and click Export Data. This would give you a JSON file which you can right click → Import Data into a blank actor in the new world.
Perhaps the thing to do first is to try and create a blank new world with Cradle of Quarts and see if that works.
If you still have issues with it, please check your dev tools console (F12) to see if Foundry is giving a reason why the module isn’t showing up in Manage Modules. You can also create a ticket in the #ticket-support channel of our Discord server and paste an invite to your world, so that we can hop in and check with you!