Thanks for reaching out to Apple Support Communities, åsa224.
We would be happy to help assist with your iCloud Photos the best we can. It seems like you've taken some great troubleshooting steps so far, but we'll also want to hav you double-check that your iPhone has enough storage to download these new iCloud Photos to your device. You can check your available device storage by following the steps in the article below.
How to check the storage on your iPhone, iPad, and iPod touch
If your device does not have enough available storage, that is likely why you are able to see the photos on iCloud.com, but not download them to your device. If you'd like to store the new pictures on your iPhone, you can free up some space by selecting Optimize iPhone Storage rather than Download and Keep Originals in your Photos Settings. The article above also includes some other recommendations to help free up space.
If you appear to have plenty of available storage on your iPhone, we suggest reaching out to Apple Support so they can look into why your photos are not properly syncing to your device. You can see your support options at the link below.
Get Support
We hope this helps.