Unless your assignment lasts for more than one year, it still fits the definition of a "temporary assignment". This means that your state of domicile is New Jersey, which means that New Jersey may tax your income you earn in Florida. However, New Jersey still allows a deduction for unreimbursed employee expenses. A temporary assignment does qualify to deduct employee expenses under the "old rules" (prior to the Tax Cuts and Jobs Act of 2018), which New Jersey still follows. But you still will file your tax return with New Jersey, unless the position becomes permanent and lasts more than a year. So, unfortunately, although Florida will not tax you on your income, New Jersey will still be allowed to do so. (Even if you move your DL and voter's registration, if it is a temporary assignment, NJ can declare you a NJ domiciliary resident and tax you).
You will not get any additional tax breaks for your situation on the Federal Tax return. The TCJA suspended the ability to deduct Unreimbursed Employee Expenses until 2026.
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