I don't see the argument here. You can easily adjust the law to force verification.
You seem to assume that "this is now final, nothing will change after that". Why would you assume this to be the case?
The slope is only slippery if the change in question makes it easier for future changes to be bad. Otherwise you're only arguing for no changes to ever be made. Does this law make forced verification easier than if this law didn't exist?
As someone who's pushed on a technical law change.... "easily" DEEPLY, DEEPLY misstates the challenges of getting the law changed. Fun fact: people who oppose something tend to get in the way.
But they could also just implement verification now, which many governments are trying to do. The idea that you shouldn't let a government do one thing because they might do another thing is flawed if they could already do the other thing.
The danger of a slippery slope comes when one change enables the next change - for example, a law mandating certain kinds of data collection enables a future decision to discriminate or control based on the collected data. But in this case, no data is being collected, there's no step happening here that enables a more dangerous later step.
If anything, I'd argue this makes it harder to implement more invasive measures later, because rather than arguing that some form of age control is necessary, Illinois will specifically need to argue that age verification is necessary over the existing anonymous system. That's harder than saying "there is no protection for children right now, age verification is the only way forward".