I relocated from Texas to Florida on June 23, 2024, started work on June 24, and moved into my apartment on July 2. When did I establish residency?

Not sure why you are worried about this----neither TX nor FL have state income tax so you do not have to enter anything about establishing FL residency on a state return.    When you prepare your federal return you can indicate that you moved from one state to the other, and enter the date that you began to earn income in FL.   It will have no effect on your federal tax due or refund.   Use the mailing address that you want the IRS to use if they need to mail you a letter or a check.

Residency is typically established when a person maintain a permanent place of abode in the state and does not have an intention to relocate again.

• Some states have a time requirement.
• Some use 183 days
• xmasbaby0 has a good point.  Both Texas and Florida are non income tax states.