As sibling comments indicate, reasons may range from internal politics to innovator's dilemma. But the upshot is, even though the underlying technology was invented at Google, its inventors had to leave and join other companies to turn it into a publicly accessible innovation.
LaMDA is probably more famous for convincing a Google employee that it was sentient and getting him fired. When I heard that story I could not believe anybody could be deceived to that extent... until I saw ChatGPT. In hindsight, it was probably the first ever case of what is now called "AI psychosis". (Which may be a valid reason Google did not want to release it.)
Which ML-based products?
> It was convenient for Google that OpenAI acted as a first mover
That sounds like something execs would say to fend of critics. "We are #2 in AI, and that's all part of the plan"
Some more details in https://www.nytimes.com/2021/03/15/technology/artificial-int...
https://www.cnet.com/tech/tech-industry/google-ai-chief-says...
That made plenty of scientists and engineers at google avoid AI for a while.