You already have a good answer from @Scott which shows what is probably the sane thing to do. But I'll try to show how you could automatize using Content-Aware Fill to expand a border around an image. In this case, it's probably not needed, but you could be dealing with images which actually had some texture worth preserving in the border.
I know from your other question about Pokémon cards what your end goal is, so I'll put in a few extra steps that will help you create an image which not only has an extended border, but also has the right physical dimensions (63×88 mm).
First you have to manually select the border. In your particular case it seems to work using Magic Wand tool with Sample Size set to *3 by 3 Average" and Tolerance set to 20 (Anti-alias and Contiguous ticked on).
With other kinds of images (like drawings) you might have to use Rectangular Marquee Tool, Quick Selection Tool or perhaps even Object Selection Tool or Select > Subject.
We'll assume you that your images are flattened and that you've clicked the yellow border with Magic Wand with the mentioned settings. Then you can start recording an action in the Actions panel. (It's a long recipe, so I won't go into every detail.)
Convert the Background Layer to a Smart Object.
This is done to protect the image from getting cropped.
Perform Select > Inverse.
Perform Select > Modify > Contract and contract by 4 px.
This is done to make sure you don't have any stray pixels selected. Won't work if they have a radius larger than 4 px.
Perform Select > Modify > Expand and expand by 3 px.
This is done to get back to the same "bounding box" as before, but 1 px smaller to crop it a tiny bit tighter.
Perform Image > Crop.
Enter Image > Image Size. Untick Resample. Input the physical width of the printed rectangle in the Width field. Press OK.
I'm guessing the width could be 57 mm, but you should try to check that. This is done to automatically adjust the resolution of the image so the image "knows" its own size. Later you can then scale the image simply by entering the wanted resolution as you know once and for all that the dimensions are correct. Or rather as correct as possible with these low res scans.
Make a Layer Mask on the layer with the current selection.
This is done to save the selection for later use.
Enter Image > Canvas Size. Make sure Relative is unticked. Anchor is in the center. In the Width and Height fields, input the correct physical size including bleed.
Pokémon cards should be 63×88 mm, so with 3 mm bleed you get 69×94 mm.
Duplicate the layer.
Select the Layer Mask of the duplicate layer.
Invert the Layer Mask of the duplicate layer using Ctrl /Cmd + I.
Rasterize the duplicate layer.
Select the Layer Mask of the duplicate.
Apply the Layer Mask of the duplicate layer.
This deletes everything from the layer, but the border, making it easy to fill it with Content-Aware Fill without any pollution from the rest of the image.
Select the opacity of the duplicate layer by Ctrl /Cmd-clicking its thumbnail.
Perform Select > Inverse.
Perform Select > Modify > Expand and expand by 2 px.
This is done to in case there is a 1-2 px border on the border.
Perform Edit > Content-Aware Fill. Use the default settings and set Output To to Current Layer.
Move the duplicate layer below the original layer.
Select the Layer Mask of the original layer.
Delete the Layer Mask of the original layer.
Perform Layer > Flatten Image.
Perform Select > Deselect.
Phew, that was many steps, sorry. Perhaps it could be simplified a bit and perhaps you would want to tweak some of the values, but this is the main idea.
This is how it looks in action:
