It the example you give, CO2 gas is not really a valuable commodity. Pressure is the valuable commodity in that example, and so it's kind of irrelevant when discussing carbon sequestration solutions.
That's not correct. If pressure was all that mattered, we'd just run compressors on nitrogen (or formation gas). CO2 has properties that make it especially favorable for flooding.
Has to be both. A random gas might interact with the oil being pumped. Why don't they just use compressed air? There must be a reason why CO2 is desirable for that application.
It's the opposite actually; CO2 interacts with petroleum in controllable ways via pressure, so engineers can change the properties of the oil and end up extracting more oil more quickly.
https://en.wikipedia.org/wiki/Carbon_dioxide_flooding