To answer your exact question about where the scratch files are on your Mac or on any drive you assign as a scratch disk, the answer is that they work like macOS cache files: They’re intentionally hidden from the user because they’re managed by the software. If a user messes with them, the software could crash.
So the only location to really pay attention to is the list of assigned volumes in the Scratch Disk preferences.
If you really want to know, and you understand the macOS file system at a technical level including hidden paths, you’ll find the Photoshop scratch files in the two places below. But even if you reach them, because of how system permissions work for that type of cache file, you won’t be able to delete them manually. You have to let the software manage them.
On a Mac boot volume, the scratch file path is:
/private/var/folders/…/TemporaryItems/Adobe Photoshop 2025/Photoshop Temp…
The ellipses ( … ) are because those folder/file names are randomized per session.
When assigned to an external volume connected to a Mac, the path is:
/Volumes/[name of external SSD]/.TemporaryItems/folders.501/TemporaryItems/Adobe Photoshop 2025/Photoshop Temp…