Moderate democrats are the majority in power, so it makes sense they are the most powerful and get what they want the most. In cases like Manchin, they get outsized power due to how tight margins are in the senate. That's how it works in a "coalition" of sorts. If Dems had a comfortable majority, they could force through more things. It's basic logic that a party with multiple different wings has to cater to the ones that are more likely to flip on them. In most cases, the left wing of the Dems will never vote for the Right, so it's a safer bet to de-prioritize them when compared to the right, who may vote right.
If the left wing of the dems had more voters (which is slowly happening by the look of things), they could exercise more power, and if they had a comfortable majority (and more balls), they could ignore people like Manchin.
As per your question, I have no idea, I dont keep tabs on every vote, but I am very confident my assessment of the situation is correct.