>Is the tree size still too big if you're only using Wordle's word list?
Yes, it's what I use.
Wordle has ~2300 words as possible hidden words, ~12,000 more allowed as guesses. To get best scores you need to sample from all ~15k words.
So, to build a tree: for each hidden word (2k), pick a guess word (15k), gain knowledge (729 possibilities, but only one per hidden/guess pair). This reduces your possible hidden list to 70-1kish. Repeat..
Worst tree is 5 levels deep, mine averages 3 levels deep, pruning and memoization is nearly nonexistant (I checked).
You now have 30M first move outcome nodes, 2k of which are wins. After second move, you have a billion plus (I've sampled these to gain knowledge of what to expect). The next few rounds push the compute time into crazy realms of time (again, I've sampled to estimate sizes).
I'd guess given a lot of computing power, it could be done, since around 3-4 levels most of the games complete. But since you cannot easily store this tree, I gave up for now.
You should be able to store the tree with best move only at each node, which is good for gaming, but loses interest for statistical knowledge of the tree.
Good luck :) Nerd sniping complete :)