Yes iCloud will sync all photos between the different devices, all devices will have the same photos.
That is the main intention of iCloud.
Introduction to iCloud - Apple SupportOfficial Apple Support › guide › icloud › icloud
I would be very careful with the term "I recently backed up my iPhone and iPad in iCloud ..."
iCloud is not a backup system, it is more a sync system.
As soon as you delete something on one device it will also be deleted from the iCloud and all other connected devices!
iCloud will protect you if something is wrong with your iPhone / iPad, but not from user mistakes.
I would recommend that you create folder for "working purposes" and for "private purposes", then you can split your files.
Organize your apps in folders on iPhone - Apple SupportOfficial Apple Support › guide › iphone › ios
If you really want to have them 100% separate you can go with 2 Apple IDs, one for the iPhone and 1 for the iPad.
Then no information will be shared between devices.
The storage issue on your iPhone can be fixed
Manage your photo and video storage - Apple SupportOfficial Apple Support › en-us
Store your photos and videos in iCloud
Your photos and videos are stored on your device in their original, high-resolution version. This means that they use a lot of space on your iPhone, iPad, and iPod touch. With iCloud Photos, you can make more space available on your device and have your entire collection, everywhere you go.
Get started with iCloud Photos:
- Tap Settings > [your name] > iCloud > Photos.
- Turn on iCloud Photos.
- Select Optimize iPhone Storage to save space on your device.
Ralf