scanning will continue when you are... no it won't

I tested this a while ago and then in my setup (macOS 12.5, Mac mini 2018) scanning people did not seem to happen unless I set Energy Saver to prevent sleep AND do NOT do essentially the same by putting the cursor to a hot corner that also prevents sleep.

Then leave the cursor in the middle of the screen (with Photos.app quitted) and leave the Mac on overnight or for just for about an hour for several new images (so the screen saver kicks in and the display turns off). Maybe a coincidence but I could repeat this several times. In Sonoma the settings GUI is somewhat different and I have not tested it there.

You may also want to check, if your Photos Library is containing incompatible or damages or missing image files. The scanning for duplicates may get stuck on images, that Photos cannot process. The usual suspects are older video files, imported in older versions of Photos or iPhoto or Aperture, while these formats have still been supported. Or items, where the original image files cannot be accessed. Are there any items in your library with blank thumbnails, or items shown in an album "unable to upload"?

The location of your Photos Library could also matter. If you are keeping the library on an external drive, this external drive needs to be connected and mounted at all times, while you are signed into your user account.

Paul Richards4 wrote:

There is no 'unable to upload' folder, and none have blank thumbnails.

My library is currently own an external drive but that mounts automatically when my mac starts up, and stays mounted continuously.

I never sign out of my account.

While there are about 48,000 items in the library, the "Finding Duplicates" function has occasionally worked previously, and in fact worked a few weeks ago, finding about 40 duplicate items which I merged and or deleted. Since then I get the message in the header, though I know that there are duplicate files in my library, it just won't find them.

And as I said, this problem has been reported by others at leas as far back as 2017... Why don't Apple address it?

Are your Settings for the Energy Saver as described by Matti? They are working for me as well.

As the duplicate detection has been working for you before but does no longer work, something must have changed in your library. Have you checked all items you have added to your library since the duplicate detection stopped working?

Whenever Photos stopped scanning my library, I found a photo or video, that is not compatible, for example a file saved from a webpage with the filename extension .webp or some photos shared with me from Mail or messages in an incompatible format, or a video I had edited with an external editor on one of my other devices. And occasionally I came across a very old image file, imported many years ago, that suddenly has gotten damaged. These item do not necessarily appear in the "unable to upload" album. I have to check the "Recents" or "Imports" album and look at "Shared with you".

Have you set the "Ignore ownership" flag on your external volume? If this flag cannot be set, Photos may encounter problems with the file ownership of the files inside the Photos Library. Trying to set this flag is the best test to see, of the external drive is compatible with Photos. It will also ensure, that you do not encounter problems with the file ownership in the internal databases, if you ever connect the external drive to another Mac. Move your Photos library to save space on your Mac - Apple Support

What format is the external drive? It needs to be formatted Mac OS X Extended, Journaled or apfs.

Questions about why Apple does things or not can only be answered by Apple, and that's who you could contact for that portion of your query.

Paul Richards4 wrote:

And I'm posting here for two reasons - to ask if anyone else has solved this, and to remind Apple (who obviously must monitor these posts) that people are still having trouble with this after seven years, because even if there is a workaround (and there doesn't seem to be one), Apple could really do with looking at this!

(and yes I reported it on the support page!)

As Yer_Man noted, Apple doesn't read here for feedback or suggestions. I also don't know what you mean by "support page". But just in case, here is the link for the feedback page that Apple does read:

Product Feedback - Apple

Anyone here who works for Apple is identified as such. The reason we write with great conviction that Apple doesn't monitor these pages for feedback and bug reports is because that's what Apple told us when we asked. And that makes sense if you actually spend a couple of months seeing the bulk of the issues posted here - a very high percentage are in the "problem exists between keyboard and chair' category. The signal to noise ratio is far too poor to yield any significant volume of useful information for the various developers. But by all means write your notes to Apple here. We're just trying to save you time and wasted effort.

Yes the format does make a difference.

This is not a reliable way of communicating with Apple. They don't promise to read anything here.