Of course, happy to.
Okay, so thanks for framing it this way.

When framed this way, this is precisely one of the kinds of "who has what power" issues and what happens when someone else tries to do something that often comes up.

Congress uses its power to create groups A and B who are taxed different (or whatever).

The groups are never perfectly well drawn.

A state comes along, and takes some folks in the "grey area", and says "yeah we're just gonna say that these folks are in group B"

(I use congress and the states because they are easy to think about, but feel free to substitute any two groups that have explicit separation of powers)

In that case, and in your first case, the answer is "you probably can't do that".

To start with, again, the normal resolution would be for the court to simply say "you can say what you want but you can't affect who gets worker's comp by what you say - period. It's not your power". The court is literally disallowed from doing this in this case

But to dive into it:
"I don't see why the ability to use a category when describing the worker's compensation scheme necessarily includes the very different power to take control of the definition of that category."

It only does to the degree necessary to effectuate the scheme and normally would only apply to the scheme (unless said otherwise).
Again, the normal path would be to interpret the provision in a way that does not cause constitutional issues, or to sever it.
But prop 22 doesn't allow this.

So normally, the court would say "to whatever degree this provision attempts to control who has workers comp, it fails at that. No matter what exists now or in the future, only the legislature gets to decide who has workers comp. To the degree the provision has any other effect, it still does".

But again, it can't here. So it appears weird in that it appears to grant one group more power. But it's not, really. It's really saying "you won't let us sever or reinterpret this, so we aren't"

FWIW - You can make arbitrarily close calls here that rub people either way.

For example - imagine the statute said "once in your lifetime, you enter your name into a computer and 1 in a trillion times it says no. If it says no, you are in group B. Otherwise, nothing happens".

This has no effect 99.9999999999% percent of the time.

It still would be struck down (and my experience is it also feels "wronger" to people than your version).

To both your hypotheticals, for starters you are taking them farther than they normally would go in most states/etc. California is a little weird here.

In the first one, in federal court, and most states, if it had no effect, you wouldn't have standing to challenge it at all, and in most places, standing is a jurisdictional bar (IE without standing, the court literally does not have the power to hear your case).

California does not consider standing a jurisdictional bar, so it may hear it anyway. So you could end up in a case in california about something that has no effect, but it would not really happen elsewhere.

The next thing that would happen is to determine who has the power to regulate this area, and have they regulated.
If it's not you, and they have regulated, you generally can't do much of anything (this is not perfectly true, but we'll dive very far into esoterics too quickly)
This is where your first hypothetical will likely get knocked out. If it's not your power to exercise, you don't get to say anything about it. The court will try to ensure it interprets things in a way to cause the least "destruction of statutes" as possible, but you don't get to say anything about it. It may do that by determining you have had no effect, etc. But it will often do it by removing the section that says anything, even consistent. This is because it avoids issues later on when the group with the power to define the scheme changes it. Otherwise, everyone will be back in court saying "well, this other things says this", and the court will have to decide again "yeah, again, they don't have the power to change that".

In the second hypothetical you give, that body actually would have the power to define who is an independent contractor for the purposes of worker comp. It will in fact, get to define everything it wants to define for the purposes of workers comp.
None of those will have any effect outside of workers comp.
and nobody could affect their definitions as-applied to workers comp.

So to the degree the legislature's definition of something affected workers comp, it would be held to not affect workers comp :)
Or it would be held entirely unconstitutional if they had an explicit no-savings clause.

It's not infrequent to see definitions that change depending on agency context and use and power because of this happening.

For example, defining "spouse" for the purposes of federal railroad benefits vs "spouse" for the purposes of "family medical leave" vs "spouse" for the purposes of immigration law vs ....