After reviewing the ML Rules, it seems that, if the Phillies offer Rodriguez a contract, they will have to add him to the 40-man roster. Rule 2(c)(8)(D) states:
Upon reinstatement, the Major League Club to which the player is reserved shall restore the player to the same status that the player had at the time when the player retired or became ineligible.
Rodriguez was on optional assignment. At the start of 2024, he had two options remaining. Fangraphs, at least, says that as of now, he has only one option remaining, so the Phils could tender him a contract, then option him back to the minors for 2025.
Rodriguez spent 8 days on the White Sox' active roster in 2023. He appeared in one game - apparently as a pinch runner (he scored one run, but had no plate appearances). He turned 24 a couple of weeks ago.