I doubt it's anywhere near the billions of dollars in cost as Alexa devices were for Amazon. The only cost here is compute power and engineer salaries, there's no hardware to design and build. I expect most of the compute power costs can be passed back to customers that pay for the system. Really it's just the cost of a modest machine learning team to build and maintain the model--this doesn't strike me as something that will be anywhere near the 14 billion dollar plus and counting sinkhole that is Alexa.
IMO this is to drive adoption. Without customers using your product, it doesn't how much anything costs; there's no revenue. Give it away, increase usership, get feedback, improve performance, and then put a price tag on it. Per usual, Amazon is tardy to the party, and must now compete against an established Copilot product (and GPT).