P: Allow us to search for similar photos in Lightroom Classic

Phones can do this because it is not actually the phone doing it but a cloud service that indexes all your images, and uses AI/ML to analyse all these images for visually similar features and returns that info. This is how Apple creates these automatic little movies for you such as "pets over the years" etc. It's not your phone doing that but a big computer in the cloud analysing all your images. Classic of course only locally stores images so this mechanism doesn't work. Lightroom Cloudy does do this on the cloud servers using Adobe's Sensei AI machine which is how you can search for features that you never keyworded. Computers are getting powerful enough with dedicated AI cores on M1 and M2 machines that conceivably you could start doing it locally in something like Classic. AI is very compute intensive.  Adobe does use quite a bit of AI on your computer already for automated masking and such but it is not training those models on your own computer. It uses pretrained models. I think the next generation of this will be training models locally where it analyses how you tend to edit your images and offer to edit in your own style instead of the auto button which is an AI that was trained by having a bunch of photographers edit images and use that as the training model. That model does locally recognize the type of image you are trying to edit (landscape, portrait, etc.) and applies more or less appropriate edits. Would be awesome if you could train this AI yourself so your images get edited in your style instead of the average of a bunch of other photographers.

For LrC, are you refering to:

• Duplicate photos with same file name, probably in different folders (LrC search can handle this)
• Duplicate photos with different file names, but mostly same metadata, perhaps renamed (LrC might handle via metadata search, otherwise, plug-in)
• Duplicate photos, different file names, different or some missing metadata (might need external software)

https://expertphotography.com/duplicate-photo-finder/

Bridge is a browser only, not (like LR) a DAM. It only 'sees' into folders you tell it to. It isn't smart like LR; there is no catalog. Of course, you can search in the catalog for all kinds of data.