If your state is an "at will employment" state then I don't see how this would be a valid lawsuit. Yes, you can sue for anything however they can hold the policy you broke against you. If your boss took money from the register and everyone else took money from the register, does it make it legal? 5% isn't much, and everyone did it, but taking a penny a day is also stealing and adds up. So...I wouldn't waste your money on a lawyer for a case you will lose. Hell, I bet you'd even lose the unemployment case. Our store has about a 98% success rate in unemployment cases.
You can sue for being terminated from your job in spite of being an at will employee but it's pretty narrow. Basically, if you're terminated because you're part of a Title VII protected class (race, gender, religion, etc.) but it has to be because you're terminated for being one of those classes. So, if your boss walked up to you and said "you're fired because you're a man/woman/muslim/christian" then you'd have a civil rights act claim against them. It's never that blatant though which is where the minutiae of proving up the reason you were fired was because you were a man/woman/etc. comes into play. Now, sometimes there's state laws that add additional protected classes but the biggies are the federal protected classes and there's nothing to indicate he was fired for being part of a protected class.
I give him pretty good odds on an unemployment case. If he can actually show up that he had the implied authority to act in the way he did and continued to act in that way under the new leadership, without them making any attempt to correct it, he has a decent shot. He could likely call witnesses (not sure about Ohio's unemployment process though) including his old leadership that allowed him to give the discounts and show that not only was it permitted previously but potentially even encouraged.
As far as people saying he should sue, just to sue, or start a class action, that's not gonna fly. The biggest reason why it's not gonna fly is because he'd have to prove up damages. When you're an at will employee, you don't have damages for losing your job. Now, if we're talking systemic civil rights violations like I talked about above, well then yeah you got yourself a class action ready to go. Here, nah, nothing that would indicate a class action.
Now, where an attorney does come into play for OP is in protecting him against them attempting to collect on that civil demand letter he signed. I'm not sure how much money they made him sign for but we're potentially talking hundreds to thousands of dollars. He can, and should, seek the advice of a lawyer to see what his options are in spite of signing that civil demand letter.
As far as bringing an action to recover damages though? Nah, nothing much really. What it's about for OP at this point for contacting a lawyer is trying to protect himself from losing money from signing that civil demand letter. Hell, if I was licensed in Ohio (at least I think his store is in Ohio, based on the store number he gave) and near there I'd be willing to meet with him in person and review his situation for nothing but I'm not so I can't help personally. I'm actually a little incensed that they did this to him as the situation seems to be. I'd love to fight them on this one but I can't because I'm nowhere near there and not licensed in Ohio.
I was totally against signing but I feel like if I didn't sign they woulda called the police and I don't think there's anything more embarrassing than getting escorted out of your job in handcuffs
The decision to call the police is NEVER dependent on whether you sign the civil demand letter at Target. If they think they have enough for criminal charges against you, they will ALWAYS call the police to escort you out, regardless of whether you've signed the civil demand letter. Any promise/threat they made you to get you to sign that civil demand letter was almost certainly a lie.
Furthermore, I'm a little surprised at the process they used to terminate you. Back when I was an APL, unless an employee was explicitly stealing for themselves, it was considered an HR term. Basically, it was only an AP internal termination if we were calling the police and pressing charges against someone. It sounds like they went through the internal investigation process, including bringing in the APBP but they didn't actually go through with calling the police and pressing charges.