Your state laws apply. Working dogs are usually exempt from leash laws WHEN working or training.
Pets are not.
Usually you find the laws and regs in one or two places - game and animal laws.
Working dogs can be herding dogs, SAR dogs, dogs used in field trials (live or drag), and permits may or may not be required. Licenses may or may not be required. You may or may not be able to work your dog depending on where you are in your state.
In other words, you can’t just let your dog loose to train it to “track” and think it’s legal unless you verified it’s legal beforehand.
If your dog switches to a live scent - it is either free ranging or you are hunting without a license.
The short answer is - check your state’s game and animal laws. If you work with your dog on public land, verify that you are permitted to work with your dog in that jurisdiction. Many parks, wilderness areas or WMA’s either restrict or ban dogs, period. Or may only permit hound hunting; and specify a training season (or not). Or only permit pets on leash. They may or may not require you to train your dog during an established training season - doesn’t matter if your dog hunts live or drag. Working with a dog on federal land has it’s own set of complex regulations and it may not be permitted at all.
Your county can even have ordinances banning or restricting working dogs except in certain areas zoned for field trials. Or not permit any form of off leash work.
Layers of laws, regs and ordinances.
If you look at the link Cammie posted - you can see an example of how complex the laws can be. In the OP’s state, the regulations change based on streets and within counties.
My state is similar. It’s really easy to screw up. You can be legal in one place, literally cross the street, and be committing a crime. It’s crazy.
I hunt on foot too - I agree. Sometimes I wish I was on a horse. My understanding is that drag lines can be faster than live.
One of the reasons for training seasons (whether live or drag) is to mitigate the impact the dog has on wildlife (even it the dog is not preying on wildlife it still impacts its environment). Another reason is to mitigate the impact on other users of public land. People enjoying the local park should not have to contend with a group of people who decide to train their hunting dogs (live or drag does not matter)