Ok, so you have moved out and there is now no continuing problem. While you could file a lawsuit against your former landlord, the question is whether you would win any money damages. Since you moved, there is no point to sue for injunction now. There are two parts to answering the question of whether you would win any money damages. The first is whether you can prove that the landlord failed in some duty that he had to you. It is not the duty of the landlord to resolve all disputes and problems between tenants. As was pointed out already, the law you cited, Florida Statute § 83.52 cannot be the basis of a lawsuit against your landlord because that section does not describe the duties of the landlord, but rather lays out the duties of the tenants. Because of that, the following statement you made is wrong:
That is quoted from subsection (7) of § 83.52. That is a duty of the tenants, not the landlord. It does not mean that you have a right to a peaceful dwelling; you are reading more into it than is there. It does mean that you would expect that the other tenant to conform to that subsection and not engage in activity that would “unreasonably disturb the tenant’s neighbors or constitute a breach of the peace.” So perhaps that statute would provide you a claim against your former neighbor, but it does not support a claim against the landlord.
The landlord does generally have an obligation to provide tenants with a right of “quiet enjoyment.” At old common law, this right only meant that the landlord was obligated to defend the tenant against other claims to possession of the property. Some states have expanded the definition of quiet enjoyment to include making the landlord liable for other things that unreasonably interfere with the tenant’s occupation of the home, including doing something about the actions of other tenants that would cause such problems. But Florida is not one of those states. It still uses only the very narrow covenant of quiet enjoyment from the old common law. In Florida, the covenant of quiet enjoyment does not cover problems caused by other tenants.
This leaves you with the problem of identifying a duty imposed by law on the landlord that the landlord breached in this instance. The statute you cited doesn’t help you nor does the covenant of quiet enjoyment (which is often where the obligation arises in other states). I have not found a duty in Florida that a landlord would have to remedy the problems you had with the neighbor. Unless you can find such a duty, you will lose if you sue the landlord. I can understand you’d be frustrated that Florida law evidently does not require your landlord to remedy these things for you, but you have deal with the law as it is, not how you’d like it to be.
The next issue is that even if you can identity a duty that the landlord owed to you that was breached here, what money damages did you suffer, i.e. what financial loss can you point to as a result of what happened? The law does not compensate you with money damage for being annoyed or upset. You need to show the landlord’s actions caused you some kind of financial loss.
The statute you cited might be the basis for suing the other tenant for money damages. The problem is, the statute itself does not say that you have a remedy for money damages from another tenant violating that statute. You’d need to find case law that says you have that remedy. And again, you still have the problem of identifying the financial loss that tenant caused you before you can win any money damages. Finally, that tenant would also need to have money or property somewhere that is not exempt from attachment under federal or Florida law for any judgment to do you any good. Getting a judgment you cannot enforce is worthless.
For what it is worth, since you have moved and the problem is therefore over, you may want to consider just moving on with your life rather than pursuing either your old landlord or the other tenant in court over this. You may spend a lot of time and money on a lawsuit that you either cannot win or that you cannot collect, which would just add to your frustration. Not every wrong in life is worth suing over even if you might have a claim to pursue. You need to pick which ones are really worth fighting over and which ones to let go. Life it too short to keep looking back at what happened to you in the past. You’ll likely enjoy life more looking forward and spending your efforts in making your future enjoyable.

