I would just not use AI in schools. Likewise, I would only have computers in a single computer lab.
We keep looking to technology to create educational shortcuts but have any of these shortcuts actually worked out? Over the last 40 years we have put more and more computers in schools and kids have become less literate, lost the ability to spell, and we've reached this bizarre time in history where it's become common to distrust basic science. The main things computers have brought to K-12 education are amazingly efficient ways to cheat and avoid actual learning.
With AI competency comes language, critical thinking, and research -- huge skills applicable everywhere, not just AI.
This is just not true. With AI comes the ability to AVOID learning any of those things.
We need more teachers. That's how we improve the success rate. That's what prestigious private schools do to prepare kids for prestigious colleges. You provide small classrooms and make tutors available.
giving education on essential tools
You are conflating education with vocational training. Treating education as vocational training is one of the major problems that got us into this mess.
Up until the last couple hundred years, having people hyper-specialize worked wonders to construct the modern civilization we enjoy. It didn't matter if a fletcher had a basic understanding of economics because he had no say. Likewise, in China they can get away with treating education as vocational training because having a broad education doesn't do a person any good (it's probably depressing, because it makes them aware of how shitty their situation is).
In societies that elect their leaders, the only thing preventing incompetent grifters from seizing control is a broadly educated populace.
Just look at how many people here on ./ are experts in highly complex fields—programmers, engineers, sysadmins, etc. And then look at how many of these dudes are complete idiots when discussing any topic outside their field of expertise.
So I guess that's a long way of saying, "You don't worry about teaching essential tools, you teach foundational concepts." Teach kids symbolic logic in elementary school. Teach them foreign languages in elementary school (most people don't really understand grammar until they learn a foreign language). Teach them how to write with a pencil and paper. Give them more teachers so they can learn these things while getting individualized attention.
As a final example, think of music theory. I have known tons of musicians who learned how to play a specific instrument, repeating songs written by others. Sometimes they're damned good at it. But they can't play other instruments, can't write their own songs, and haven't the faintest clue how to improvise. I have also known tons of musicians well versed in music theory. They can play any instrument (although technique will vary depending on instrument), write songs on any instrument, and improvise on any instrument within minutes of picking it up. Why? Because they didn't learn to use an essential tool, they learned a fundamental concept. If you're starting a band, which musician would you prefer?