Can I search for duplicates in my Photos library

You don't say what computer you're using or which MacOS you have. In the newest MacOS, Ventura, Photos scans all the pictures and puts the duplicates in a special folder, like this

It shows the duplicates together, and you can have Photos put one in the Recently Deleted Folder where it will be automatically erased in a month. If the pictures look the same but have different sizes or metadata, you can choose to merge them, taking the best parts of both. Or, you can deal with them in your own way, which is what many of us do, since "taking the best parts" is a bit ambiguous. Some pictures may be very much alike, but maybe taken seconds apart, so you have to look closely.

If you have no duplicates, or Photos hasn't found them yet, then the Duplicates folder won't be shown.

Sadly, this function isn't available in older OSs.

Here is the link to the page in the Photos User Guide:

Remove duplicate photos in Photos on Mac – Apple Support (UK)

Photos is not really only looking for duplicates, but for redundant photos - it is showing exact duplicates but also similar photos.

On older system versions you can find the duplicates or similar photos indirectly - by looking at the "Days". Photos is suppressing the duplicates and similar photos from the curated Days view. All photos omitted there are candidates for removal.

Yes you can Mohawk. Here’s how to;

1. Open the ‘photos’ on your iphone and tap Albums.
2. Scroll down and tap Duplicates below Utilities.
3. Duplicate photos and videos appear next to each other.
4. Tap Merge to combine the duplicates, then tap Merge [number] Items.
5. Merging combines the highest quality version and all of the relevant data across the duplicates, and keeps that one in your library. The remaining duplicates are moved to the Recently Deleted album.

If you do not find the “Duplicate” option, then you do not have duplicates.