Does "Download and Keep Original" require manual sync of each photo?

To downloads all photos, Download and keep originals will retrieve all images from the cloud and save them to your phone. Optimize storage will only download when photos are viewed and/or are needed by an application.

It may require you to plug your phone in, connect it to Wi-Fi and wait for a bit for all of the photos to download, as you said there are quite a few. It may help to have Photos open beforehand too.

Source: Experience & Apple Support documentation.

In some cases waiting does not help (there are multiple threads about it on apple forum. )

What worked for me to force downloads was to select as many pictures as I could and choose to share them (for instance via AirDrop). That required iPhone to download originals which I later synced via photos (sharing won't work with live photos)

It does work in the background and can take some time. If you turn off icloud for photos and get a message warning you that x number of photos are still not downloded, then you know it’s still downloading them. Cancel and check again later....