As you note, the software industry lacks meaningful definitions of "productivity." We talk about it as if we agree on what it means, but can't measure it or compare it across teams, projects, or business domains.

Studies I've seen thrown around come from companies such as Microsoft and OpenAI and Anthropic, all of which have deep vested interests in pushing the AI productivity narrative, so I hesitate to trust them. Digging in, their data seems either anecdotal or based on the kinds of mostly-useless metrics you listed above.

We won't know for years, maybe decades, whether AI tools benefit or hinder software development. Probably some combination. I think the most serious follow-on effect of AI in software development will come from the short-sighted decision to hire fewer junior programmers, which will lead to a shortage of experienced senior programmers. Executives and investors won't feel that pain for a while, they can cash in their shares and options today. Supply and demand will raise salaries for senior programmers, and the shortage will impose delays and opportunity costs. Those costs may outweigh whatever short-term and I think superficial gains AI tools may offer now.