It would be difficult to devise this political scenario.
You can't make "contracts" work without some sort of collective, one that is more powerful than either Party in the contract, to enforce the terms of the contract, and typically to restrict the terms allowed in contracts.
Without such an entity, the more powerful Party in the contract can violate it at will; without punishment. For a contract to be any more than an empty promise, the weakest Party in a society must have some Court system they can use to force any other Party in a contract, even the most rich and powerful, to comply with the terms of the Contract. At least a credible threat to do that.
You also have the problem that Rights are enforced by the State, and these indirectly (by various court decisions) restrict what we can even make Contracts to do: In the USA, you cannot have a contract that requires somebody to break a law, or allows an employer to break a law.
For an example of the latter, a USA employer cannot have their employment contract say the employee waives their right to sue for sexual harassment (Heck, if we allowed that, I'd bet money some employment contracts would require sexual favors as part of the job.)
A private (meaning non-governmental) employment contract cannot force employees to accept violations of workplace safety, they cannot require employees to risk their lives (or sacrifice them). (Such requirements can be part of military service, but are treated differently, and other restrictions still apply: On the front lines a commander can order a female soldier into lethal combat, but cannot order her to have sex with him.)
Contracts are useless and meaningless to people that have zero chance to appeal to power to get them enforced. They are empty promises to the 99% if the only people that can enforce them are the rich and already powerful.
Without enforceable restrictions on what terms are allowed in the contract, the rich and powerful have you trapped and can collude so there IS no alternative: For example, every State contract (by agreement of the Rulers of States) demands 90% of your income. None of the States dare allow anything else even if they wanted to: The rest of the States have agreed to shut down all Trade with any member that does that.
By collusion among States with greedy and power hungry leaders, I think your system will quickly develop into a lot of oppression and slavery with no escape for the citizens. Sure, they're free to switch from one slave owner to another: But their contract says to do so, they must pay a fee equivalent to five years of their salary; and every State's contract says the same thing.