If the black border color is completely uniform, one technique to try is the Image > Trim command. It looks at the color of a corner pixel, and crops out all contiguous pixels of the same value, such as black. It stops when it reaches a pixel that is not the same value. But, this can be unreliable if the border color is not uniform within a scanned film frame.
For very large numbers of scans, I avoid Photoshop because it’s far too inefficient and slow. Partly because each image has to be opened one by one. Doing hundreds of film frames takes forever.
I strongly prefer using something like Lightroom Classic or Adobe Bridge + Camera Raw. In those apps you can quickly bulk crop (and bulk correct) any number of images at once, as long as the scans are in a supported format such as raw, DNG, TIFF, JPEG… (In Camera Raw, you must enable TIFF/JPEG support in File Handling preferences.)
The key is to select all of the images, so that an edit affects all selected images. Hundreds of images can be corrected in seconds. Below is a demo of that. As you can see, it works even better if the border is consistent across scans, because the same crop works for all of them. When finished, you do have to export copies from Lightroom Classic/Camera Raw with the crop applied, because in those apps the crop edit is only in metadata (to preserve the original).
Steps shown in the demo:
1. View folder in Adobe Bridge. There are 29 TIFF scans.
2. Select all of them and then choose Open > Camera Raw.
3. Select all images in the Camera Raw filmstrip, and switch to the Crop tool.
4. Crop one image. All selected images are cropped the same way (watch the filmstrip).
5. Make tone and color corrections. All selected images are corrected the same way.
6. Make sure all images are still selected, and click the Save icon to batch-save new copies with these edits applied. Batch save is GPU-accelerated in Camera Raw and Lightroom Classic.
One reason Camera Raw and Lightroom Classic can do this faster than Photoshop is that those apps can process multiple images simultaneously, and the more CPU cores the computer has, the more images they can process at the same time. But in Photoshop, even a batch automation is going to process images serially, one by one, and that’s always going to be slower.
For bulk scanning jobs, I only move a photo to Photoshop if it needs specialized retouching that Lightroom Classic or Camera Raw can’t do. But I’ve edited fewer and fewer images in Photoshop as Lightroom and Camera Raw retouching and masking tools have improved.
If you don’t want to have to adjust the crop manually, or if you must do it in Photoshop, someone might be able to suggest a Photoshop script of some kind that could try to auto-detect the border, make a selection based on it with a little tolerance, invert the selection so that the image is now selected, then run the Image > Crop command on that. But that might fail if the image itself has colors similar to the border that also touch the border.
On the question of the round corners, I’m not sure. I feel like if the round corners are there, a little of the border should also show; if the idea is to remove the border then I think the round corners have to go too. But it’s really up to you.
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