How much extra water and time is needed when cooking rice with a tomato-based liquid/semi-liquid too?

I think it's hard to estimate an exact ratio for the process you described, as tomato paste, tomato sauce and tomato soup all have varying water content, probably even between iterations of the dish. I would take a "risotto-style approach" here (or similar to Indian dhal): start cooking the rice with the other ingredient, reduce to low-medium heat, then regularly stir and replace liquid that's absorbed or steams off until the rice is done to your liking. I would maybe use a light vegetable stock instead of pure water that's kept at a simmer to maintain the temperature better.

The reason: there's too many variables here. If there are additional vegetables with high water content in the dish, this might require less liquid, etc. It is slightly more work because you need to keep an eye out for the doneness and liquid level, but it should be relatively foolproof.