As for what your individual prompts contribute, it is impossible to get good numbers, and it will obviously vary wildly between types of prompts, choice of model and number of prompts. But I am fairly certain that someone whose job is prompting all day will generally spend several plane trips worth of CO₂.
Now, if this new tool allowed us to do amazing new things, there might be a reasonable argument that it is worth some CO₂. But when you are a programmer and management demands AI use so that you end up doing a worse job, while having worse job satisfaction, and spending extra resources, it is just a Kinder egg of bad.
[1] https://ourworldindata.org/grapher/annual-co-emissions-from-... [2] https://en.wikipedia.org/wiki/Gas-fired_power_plant [3] https://www.datacenterdynamics.com/en/news/anthropic-us-ai-n...