God, being the source of all, is surely not in need of rest; being limitless, it seems he could do anything without effort. Why, then, does the text say in Gen 2:2 that he “rested”?

Indeed, it is very probably not because he needed a rest. Probably, the traditional explanation is correct: he was demonstrating to mankind what man should do: observe the sabbath, the weekly day off. The following sentence underscores this. The text anthropomorphizes God in this way, in a few different places, e.g., when it says “repents” and is “grieved” that he made man, on Gen 6:6. There are also physical anthropomorphisms; perhaps indeed God has no literal “face,” despite being said to have one (e.g., Lev 20:6).