Unable to download photos from SD card to Photos app on iPhone

Are the files on the SD card stored by a camera, or at least organized in a DCIM folder with subfolders as a camera would arrange them, named as a camera would name them? Photos will do some "sanity checking" on the folder structure and the files before trying to interpret them as camera output. (The nature of the checking is undocumented and seems to vary from release to release.)

Here's a guess: The Files apps treats files as files. They can be .jpg or .doc or .xlsx or .pdf or whatever. Photos expects picture files, and it doesn't see any of those. You didn't say anything about what was on the SD card or where it came from, so it's pretty hard to know for sure, but one thing you could try is re-formatting the card.

ExFat and Fat32 are fine for static storage. You would run into problems having a dynamic system like a Photos Library on that format, but this is fine for a camera. It's unlikely the camera can read Apple's formats.

It really does sound like the Photos app on the phone is failing to recognize those files as picture files for some reason. If you load them into Files, can you save them to Photos? Select them and Share>Save nn Images? If that works, then you can delete them from Files. It's an unfortunate extra couple of steps.

Can you see the pictures with the SD card plugged into a computer?