HOW TO VIEW ICLOUD PHOTOS/VIDEOS ON YOUR BRAND NEW MAC

For Mac see the articles https://support.apple.com/en-in/HT205749

https://support.apple.com/en-us/HT208682

You have turn on photo box in system preferences > iCloud > https://support.apple.com/en-in/guide/mac-help/mh36834/mac

When you set up photo library and its preferences in Mac https://support.apple.com/en-in/HT204264

https://support.apple.com/en-in/guide/photos/pht5156cc968/4.0/mac/10.14

You don't need to sign again and again with Apple ID and password at www.icloud.com and select photos if they are uploaded , select them and download each or selecting multiple photos , photos will automatically sync when photo library and its preferences are set , the only settings to be set is unmodified originals https://support.apple.com/en-in/guide/icloud/mmb5dbaf376f/icloud

Use the same in settings in photo preferences of photo application .

for iPhone , if same Apple ID and password is signed on the same network , the photos will sync when photo box is turned as on https://support.apple.com/guide/iphone/use-icloud-photos-iph961b96c4d/ios

FIRST, stop shouting.

WHY IS THIS SO HARD?

This is iCloud Photos works. And your iPhone works the same way. iCloud Photos is a syncing service, not off device storage.

There is no iCloud only option for any of Apple's Photos apps despite what you believe. Apple does not offer editing in the cloud either, which seems to be your goal.

There is optimization that reduces the size of the photos on your phone but not remove them entirely. Facts matter.