"Download and Keep originals" setting doesn't help: photos keep downloading every time I go to albums

Hello, dear Apple community!

I got new iPhone 15 Pro and synched it with iCloud. I want my old pictures and albums to be on my new device permanently so that I always have access to them, even without connection to the Internet. But every time I go to albums, they keep downloading. I get the icons of iCloud even after I already downloaded (by scrolling down and waiting for the iCloud icons to disappear) this album a few hours ago.

My settings in Photo are set to "Download and Keep originals".

Could you please tell me what can I do with the settings to just stop this from happening and have my albums with me at all times, but not turning off the synch to iCloud (because I want the new pictures backup)?

Thank you for your time!