Downloaded photos and videos remain in iCloud after transfer to new iPhone

If you are using iCloud Photos, all of your remain in iCloud and on your devices, and changes made will reflect on all connected devices. If you delete photos in iCloud, they will also be removed from your iPhone.

But you can transfer your photos to your computer before deleting them in iCloud Photos, to reduce the storage space in iCloud:

Archive or make copies of the information you store in iCloud - Apple Support

Also check this article about it:

Downgrade or cancel your iCloud+ plan - Apple Support

A bit more information (that's a little different from the Links that Ingo2711 provided):

• If you haven't ever turned on "Settings>[name]>iCloud>Photos>Optimize" then your pictures are all on your phone, and you can turn off "Sync this Phone" for Photos. After turning it off, I'd go through my phone, and I'd go to iCloud.com, and I'd double check that everything is as expected. Then you can get rid of iCloud.
• If you have ever turned on "Optimize," then at least some of your pictures aren't fully on your phone, but you can force them to download from iCloud. First Make Sure You Have Enough Room On Your Phone! Then force the download by selecting your pictures, probably in bunches rather than all at once, and choosing "Share>Save to Files." It will download the pictures BEFORE it saves. So after downloading, it'll ask where you want to put them. Just Cancel! Then as above, go through the phone, and go to iCloud.com, and double check that everything is as expected. Then you can get rid of iCloud.

Be sure to see Ingo2711's referenced link:

Downgrade or cancel your iCloud+ plan - Apple Support