What you described can be (and is being) achieved by agentic systems like Claude Code. When you give it a task, it knows to learn best practices on the web, find out what other devs are doing in your codebase, and it adapts. And it condenses + persists its learnings in CLAUDE.md files.
Which underlying LLM powers your agent system doesn't matter. In fact you can swap them for any state-of-the-art model you like, or even points Cursor to your self-hosted LLM API.
So in a sense every advanced model today is AGI. We were already past the AGI "singularity" back in 2023 with GPT4. What we're going through now is a maybe-decades-long process of integrating AGI into each corner of society.
It's purely an interface problem. Coding agent products hook the LLM to the real world with [web_search, exec_command, read_file, write_file, delegate_subtask, ...] tools. Other professions may require vastly more complicated interfaces (such as "attend_meeting",) it takes more engineering effort, sure, but 100% those interfaces will be built at some point in the coming years.