Getting incorrect output from ADC over SPI in Arduino Uno
I am leaving this answer in case anyone stumbles across this question in the future

In a super frustrating, anti-climactic end, it turns out that the ADC chip itself was not working properly. I tested the (faulty) chip using the code above and observed the output of data pin on the oscilloscope and the output was the same square wave irrespective of the input. I managed to find a new ADC and I tested it and it was working correctly. But this raises a new issue for me, this is the third ADC chip I tested that was working correctly, the first two were faulty. It is very unlikely that it is a manufacturing issue and I used the same connections and the same code to test all three of them. Maybe it has to something to do with soldering, because AFAIK that's the only thing that's different.  If anyone knows anything else that might have gone wrong, I'm all ears.