Apple has supported OpenEXR for a number of years through ImageIO / CGImageSource, and APIs like UIImage that layer over the top. As of 2-3 years ago, there was also added low level access in the form of libAppleEXR.dylib #include <AppleEXR.h>, which may be preferable if you need to monkey with metadata or deal with channel formats which do not map well to RGBA/XYZ/YCbCr. Apple made considerable improvements in this area to ImageIO for Ventura, so you'll have to decide if that is just fine. As Ventura is this week still quite new, likely you can't rely on it being installed everywhere. For cube maps, mipmaps, ripmaps and other more GPU-ish formats, you'll definitely want to use libAppleEXR.
The overall hierarchy these days is the heavy lifting is done by AppleEXR, ImageIO calls that, and CoreGraphics/AppKit/UIKit/vImage call ImageIO. Support is identical for MacOS/iOS/tvOS/watchOS.
Support for EXRs linear colorspaces was also improved in Ventura. Before that, the tone mapping is likely to just involve clipping if you don't draw to a extended range drawing surface.
If you actually want to use the OpenEXR library APIs from your app, you'll need to download the source and build that for your machine. ImageIO and libAppleEXR provide C-level programming interfaces and couldn't adopt OpenEXR's C++ interfaces for inclusion into a system library due to the usual C++ issues with stable ABI.