Moving iCloud to new phone

No easy or good way that I know of.

One painful option for at least some things would be to manually download data to a computer and then manually upload to the new Apple ID. The following might help with that: Archive or make copies of the information you store in iCloud - Apple Support

Also note that the billing for iCloud Storage for your old ID will continue until you cancel it. Cancel by downgrading to the free 5GB plan: Downgrade your iCloud storage - Apple Support

Not sure why you had to set up a new Apple ID but having more than one Apple ID is almost never a good idea.

iCloud storage plans are linked to the Apple ID that you use for iCloud, not to specific devices or to a cell phone number. If you are signed into iCloud with the same Apple ID on your new iPhone, you should have the same upgraded storage plan.