Forcing the Photos app to download new photos from iCloud?

Have you checked on your iCloud webpage, if the new photos have already been synced to iCloud?

You may want to open your icloud webpage at www.icloud.com in a browser window on your mac, sign in with your iCloud AppleID and open the Photos.app there. Have the photos already arrived in iCloud or is twww.icloud.com with uploading?

You may also check, if you are still having plenty of free cloud storage and there is no problem with your Apple ID icloud account.

Usually Photos for Mac will automatically and instantly download new photos from iCloud, as long as all photos from your Mac have been uploaded to iCloud.

The system version you mention macOS 10.15 Catalina is rather old, three major system upgrades behind. If your iPhone is running iOS 16 it could be a problem with the compatibility. Did you by any chance enable the Shared iCloud Photos Library on your iPhone and set it up to share new photos directly from the camera to your shared iCloud Photos Library? These photos will be removed from your iCloud Photos Library. In that case you will not be able to see the new photos on your Mac, as Photos 5 on Catalina cannot access the shared iCloud Photos Library at all.

tmlen wrote:

It would be useful to be able to take a picture on the iPhone and then look at it on the Mac soon afterwards, but this seems to be impossible with the Photo app.

I do that fairly regularly. Maybe not so often that I see any issues. I think there is sometimes a momentary delay.

In the iOS photos app, it is possible to drag the photos library view upward, and then it will immediately upload them to iCloud (which also sometimes doesn't work it seems). On the Mac Photos app it just says "Last Synced at 08:51" (more than 12 hours ago), and there seems to be no button/menu etc to force it to resync.

I think I remember seeing that, but I’m not at a Mac to check.