SD card reader not working

I understand that. I have one myself (the SD to lightning version)

Unless Apple has changed things, the reader is designed to pull images from a card. To be seen the images must be in a folder named DCIM (like your camera would do) and have an 8 character name (DSC_1234 for example)

The description of the adapter you have insinuates that as well

https://www.apple.com/shop/product/MUFG2AM/A/usb-c-to-sd-card-reader

If the images you have on that card are properly formatted and the ipad still isn’t seeing it then there may be an issue with the reader.

This may take some digging and googling but you are right, the camera should automatically format the card correctly.

the one thing I wonder about is your card. I’ve had some issues in the past where readers have issues with SDHC, SDXC and the such. May not be the problem. A newer reader like this may not have the problems of others. It may also be possible that the reader isn’t working right.

What should happen is, when you plug the reader in, your photos app may or may not open, or if you open it, you will find a ‘import’ option in your photo app. That’s where you’d see the photos on the card.

Import photos using Apple camera adapters - Apple Support

Unless things have changed the SD reader is meant to read from a camera. So have you tried to take a photo on the SD card and try to read it and see if it works?