All photos not transferring from icloud

Welcome to the Apple community.

If you have iCloud photos enabled on your previous phone and your photos were sent with your iCloud library, then those photos will not be part of your backup.

In order to sync the photos in your iCloud library to your new phone, you will need to enable iCloud photos on it.

Settings ➔ Photos ➔ iCloud Photos

Yes, it will still download them except that they will be in an optimised state.

This means that depending on how much space you have available, some of the photos may be compressed. This means that while they are there in your library on your phone, they take up very little space. If you try to view them, the full resolution version will download, so you will see it properly.

What does it say at the bottom of the photos window?

Yes

I'd just let it run for a while. initial syncs can take days for large libraries. Each time you interrupt it, it may start again or it may do uploads in bits and pieces.