Pairing slim folio

In using an iPad Air1 (as inferred from the tags appended to your post) I presume that you are attempting to pair a Bluetooth keyboard with your iPad.

These article from iMore and Apple may be helpful with troubleshooting Bluetooth pairing issues:

https://www.imore.com/how-use-bluetooth-keyboard-iphone-and-ipad

Pair a third-party Bluetooth accessory with your iPhone, iPad, or iPod touch - Apple Support

What Logitech Slim Folio are you talking about? Have you contacted Logitech support team and explained your problem?

And, most of all, on what iPad model? :--> Identify your iPad model - Apple Support

If your product list (at the bottom of your original question) is correct, Apple doesn't sell any keyboard for an iPad Air 1st generation, except this one:--> https://www.apple.com/shop/product/HLPU2PA/A/logitech-keys-to-go-ultra-slim-keyboard?fnode=c5f8c2a238d399e0209273d14fc0f252e748b2251accb4893af27c0507aa95741544881b392bba304f7015f3a10804b390e2640daf5b4d700f9d3df177dd037dfc3380a6ea7d9a92f8893d0c1460e7ca75cc81f876ce47194ee8d73795721617561d3c3e49e89dbbef7f62f1d5d20da4&fs=f%3Dipad5gen%26fh%3D35d5%252B3fc3

Regards

Giulio