A couple things.
The big one is--don't practice too much against bots. Really, they don't prepare you for the real thing very well.
But setting that aside... you should always think about what you want to do with your deck. Okay, big picture, you want to win. You want half the VP (or close to half) before your opponent gets there.
Right off the bat, we see Smithy. You probably know that just buying Smithy and money nets you, on average half the Provinces in 15 turns (with luck, a little better, with bad luck, a little worse), which of course puts you well on the way to winning in games like this, where there are no VP chips or alt-VP cards.
Here, it doesn't look like you beat that, unfortunately (you buy Provinces 4 and 5 on Turn 16). This means your deck wasn't good enough to beat our baseline strategy of Smithy + Big Money. Let's see what you did wrong.
(Erm, you did nothing on Turn 1? Okay, well, that was just a mistake, or something?)
So, right away I see a problem--you want Workshop, here! If you're going to outrace Big Money, you need to pick up components for your engine really rapidly. Gainers are your friend, and extra buys are your friend. Workshop can really soak up Throne Rooms and Smithies here, allowing you to spend your $5s on Festivals, maybe with a Laboratory or two sprinkled in. Library works well with cards with give +actions and don't replace themselves (like Festival), but Smithy is cheaper and is probably accomplishing much the same thing for you here.
Now, even playing this engine fairly well, it may not be enough! That's because engines need to do something, other than buy lots of Provinces. In engines with better cards, you can reduce the price of everything to $0 and buy all the Provinces at once (King's Court-Bridge), you can earn unlimited VP (Monument, Goons), you can trash all your opponents cards (Swindler, Saboteur), etc. Here, what can you do that makes the engine worth it? Two things, basically: 1) build up to about 2-3 megaturns where you buy multiple Provinces and Duchies, likely stealing the win from behind, and 2) constantly attack your opponent with Militia. This second thing is very non-trivial. Money decks have a very hard time getting to Province without a full hand. For you, it's not about buying multiple Militias (although you might get 2 here), it's about playing 1 every turn. And with Workshop, Throne Room, Smithies, Festivals, and Labs, you should easily and quickly be able to get there. The Militia slows your opponent down, and gives you time to make your engine worth it.
I would open Militia/Workshop here on 4/3 split. The much, much worse split here, 5/2 is trickier. Probably Festival/nothing is best, allowing you the chance to pick up the all-important Workshop next shuffle.
