I would probably look into handywork, carpentry, plumbing etc

Go to trade school. That's the only thing that will be safe for the relative short-term. But a lot of people are going to be going in a couple of years. So I suggest you start now.

Everyone will be able to use the tools that AI offers without much specific training. There won't be much benefit to specific training other than understanding the vocabulary to get the tool to do what you want it to do.

If everyone will be proficient in using the tools offered by AI, what will the labor market look like?

There won't be one. Lol

Everyone is equal

No, not everyone will use those tools so there still will be somewhat of a market I think. But it's going to be much smaller than I suspect many people actually think.

Thats my q. How to stay in this smaller market.

Use LLMs every day. Use it to plan your meals. Use it to help with personal problems. Use it to feed your curiosity.

You'll build an intuition of how they work and you'll be quite valuable during the transitional period where we have AI but not all companies have adopted it to their systems.

Of course trade school, construction, etc are all viable. But you can do both if you want.

*standard disclaimer for all advice that if it ruins your life it's all your fault for listening to a stranger on the internet.

The fact is the situation is going to be different for everyone. For instance, if someone is 46 vs. 23, they probably don't want to go be a roofer. You might say nursing, but if bad smells and blood really bother you, that won't work.

Also, we could say go learn to use this new AI tool now, but two weeks from now something could render that other tool obsolete. It's really just going to be a matter of keeping your ear to the ground to see what's coming and try to leverage what you can.

In general, anything requiring decent dexterity or empathy could take a bit longer, but robotics aren't as far behind as most believe.