How is this actually restricting speech? It's not restricting advertisements for labor, it's restricting intentional lies made to misdirect. That's called fraud.
Sorry, but how would you ever prove a job ad is fake?
"Were you going to hire someone for this role?" "Yes." "Case dismissed."
I suggest people just take a credibility approach. As an example, I no longer bother with HN's "Who's hiring", everything there is bullshit.
Besides, job sites are just social media, their purpose is not to inform, it is to create eyeballs to advertisers. You should discard them, like you should also cancel Facebook, Twitter and WhatsApp.