Can't record videos using iPhone camera as it shows full even though iCloud has space

You are a little confused. You can have all the space in the world in iCloud, but that does NOT add space to your phone. iCloud is a syncing service, which let's you sync more data with iCloud, but it can never add space to an iPhone.

Open the Settings App > General > iPhone Storage - what does it say you have available on your phone? Chances are you are low in storage on your phone, which is why you are not able to record a video. If that is the case, you'll have to delete things you don't need or use, such as photos, videos, music, files, apps, messages, email, etc.

People often buy more iCloud Storage, believing it will solve their storage issues on their phone. It can't do that. Read this to better understand the difference --> What's the difference between device storage and iCloud storage? - Apple Support

iCloud is a syncing service, not a backup. If you have, for example, a half TB of storage on your phone, then a half TB is all you're ever going to be able to store in your iCloud space.

The only way to change what's stored on iCloud is to delete items on your phone to make room. BUT!, as a syncing service, anything you delete from the phone will also be deleted from your iCloud storage space.

In order to get the space on your phone to make new recordings, you're going to have to make copies on your own local drives. Like an external SSD. Then you can delete videos on your phone since nothing will change on the SSD.