Is Wordle always beatable under optimal play?

Yes, any valid Wordle puzzle will always be beatable with optimal play, as proven by Absurdle being solvable in 4 guesses.

Absurdle is an adversarial variant of Wordle where the game changes the secret word after each guess in a way that still matches the information from previous guesses. In the site's own words:

Wordle picks a single secret word at the beginning of the game, and then you have to guess it. Absurdle gives the impression of picking a single secret word, but instead what it actually does is consider the entire list of all possible secret words which conform to your guesses so far. Each time you guess, Absurdle prunes its internal list as little as possible, attempting to intentionally prolong the game as much as possible.

It's important to note that there is no randomness to Absurdle. The game will simulate the worst-case scenario* by considering every possible Wordle answer and picking the one that gives you the least information for any given guess. Therefore, since Absurdle's simulated worst-case can be solved in 4 guesses, we can assume that any "easy mode" Wordle should also be solvable with optimal play.

^{*Technically Absurdle isn't always the absolute worst case scenario. However, any extra challenge an optimal Absurdle would provide should be offset by 2 extra guesses allowed by Wordle's 6 guess limit}