Photos does not finish indexing

I am having this issue as well. In a catalog of 35,000+ images, I've been stuck at "663 photos" for days (a week, probably). I have 656 videos in my library, so I assumed the holdup was related. Like you, some of my videos have faces detected, some are named, and some seem undetected. Nothing looks wrong in the console. I only have 3 memories, which seems weird for how long it's been indexing. But the thing that makes me think that this process will truly never finish is that the photoanalysisd process in Activity Monitor has gone to literally 0.0% of CPU usage.

Check the Console.app if you can see, what Photos is currently doing. The Console can be launched from Applications > Utilities.

Select "Diagnostic / Usage" in the sidebar of the Console. Enter "photo" in the search field of the Console and enter the Return key.

Can you see any messages of the photoanalysisd related to categories, faces, or Memories? If you click one of these messages, does it show the filename of a video or a photo being processed? Frequently Photos is hanging during the face detection, because the library contains videos with a codec that cannot be processed. The face detection for videos is taking a very long time. For my library the 100 videos caused the face detection to hang for two days, before I could see any further progress. Do you have any videos In your library?

If you can see that the photosanalysisd is already trying to create memories let it simply run. In my library the scanning for memories started, before the face detection message went down to zero. Photos had already finished the faces scan, but did not update this message.

You can see from this Console message, that Photos already started to create memories. It is not really necessary, that all faces have ben detected, before it will create memories. With only roughly 200 photos left to detect faces in, you can start to merge and name the already detected persons using the "Add People" button at the bottom of the People album.

Standard granddaughter phone videos.

If that are not too many of them, open the videos in turn and check, if Photos started to assign faces circles to them, or if none of them have been processed.

I'm not sure what information one gets from that, save that it is doing 'something' with the memories feed.

I have been hoping for some messages, that contain the name of the file that is currently processed. If the filename of one image or video would appear repeatedly, we would be able to see, which item may be preventing the further analysis.

You could try to remove temporarily all videos from the library where no faces have been found (export them with "File > Export > Export unmodified original") and then see, if this will speed up things.

Assuming Photos to be reliable,

Photos is probably reliable, but if the library contains an item that cannot be processed, because it is damaged or incompatible, Photos may try over and over again to process it whenever it starts up, and then give up and not proceed to the items it could process.

This can happen, if your library has been migrated from iPhoto or Aperture. Then the library may contain images or videos in older formats that Photos would not allow to import, but they are in the library, because they have been imported by Aperture or iPhoto.

I had to remove a few TIFF files from my library because they had an incompatible color profile assigned, some BMP files sent to me by Windows users, also a few PICT files. Three videos needed removing.

I found some suspicious items by creating a smart album "photo is unable to upload to iCloud Photo Library". This collected a few items with an incompatible format.

I don't use iCloud Photo Library. Can I create such a smart album usefully without using it?

Yes. You do not have to enable iCloud Photo Library to be able to create this album. It will just list all items with a file format incompatible with iCloud, and this tis pretty much the same as the formats that cannot be processed by Photos.

It not clear from the message , if Photos should be running or not. The message says "when you ar not using the app", whatever this means. I noticed that photos kept scanning for faces even when it was open, but I did not interact with it, so switched between keeping I open and quitting it. I still cannot say for sure, if we need to quit Photos or not - try both.