You need to have some avios in your QR account to search for avios fares through them, so that might be part of the problem. Try transferring some over and see if things change. You can always transfer them back again later.

I'm not sure there's too much benefit in booking the flights and stopover hotels as one package, compared with separately. It may even be more expensive. And trying to search that way may (or may not) also impact the payment options offered.

You would need to book the.flights through QR to take advantage of the Discover Qatar rates. But those flights may also be available through BA as codeshares so that’s another booking option which may or may not be cheaper (although that way would require booking hotels independently).