Apps won’t load after buying more storage

When you purchased more storage, that was iCloud storage, it was not storage on your iPhone. You cannot get more storage on any iPhone. Each Apple device comes with a set amount of storage that cannot be changed. You have two options:

• Buy a new iPhone that offers more storage, or

• Optimize the storage on your current iPhone. You can do this and possibly free up space, by deleting apps, deleting old photos you no longer need, old emails & messages. You can read more about it here: How to check the storage on your iPhone and iPad - Apple Support

It is not possible to buy more storage for an iPhone; it will never have more than it did when you bought it. What you bought is iCloud+ storage that is used for backing up and also for syncing to other devices. Here is an explanation→What's the difference between device storage and iCloud storage? - Apple Support

iCloud+ has 2 independent functions. iCloud backups, and iCloud sync. It’s confusing because they both have the same name prefix. But they have no connection with each other. Go to Settings/[your name]/iCloud. You will see a bunch of switches (with iOS 16 or later also tap Show All). When you turn on a switch that data type will sync to iCloud. If you do this on multiple devices that share an Apple ID the selected data will sync to all of those devices. 

You can also turn on iCloud Backups. This will back up your phone every night if the phone is plugged in, connected to Wi-Fi and locked.

But note that these are independent functions; anything that you sync by the first method will be excluded from the iCloud backups.

If you are using iCloud Photos, you can turn on the "Optimize iPhone Storage" option.

This will let the phone use substitute low-quality ("space saving") copies of some photos when it starts to run out of device storage. Assuming that you have enough iCloud storage space, the full-resolution photos will remain in iCloud, from where the phone can retrieve them, on demand, later.

Do not manually delete photos from your iPhone thinking that the iCloud copies will stick around. iCloud Photos is a synchronization service, so if you delete photos from your iPhone, that is taken as a request to delete them from all devices synchronized through iCloud Photos, and from iCloud itself.