Sure, let's look at that lawsuit.

Steam Key Price Parity Provision. Valve nominally allows game publishers to make some limited third-party sales of Steam-enabled games through its “Steam Keys” program. Steam Keys are alphanumeric codes that can be submitted to the Steam Gaming Platform by gamers to access a digital copy of the purchased game within the Steam Gaming Platform, even when the game is not purchased through the Steam Store. Steam Keys can be sold by rival distributors including the Humble Store, Amazon, GameStop, and Green Man Gaming.

But Valve has rigged the Steam Keys program so that it serves as a tool to maintain Valve’s dominance. Among other things, Valve imposes a price parity rule (the “Steam Key PriceParity Provision”) on anyone wanting to sell Steam Keys through an alternative distributor. Put explicitly by Valve, “We want to avoid a situation where customers get a worse offer on the Steam store.” But that is equivalent to preventing gamers from obtaining a better offer from a competing distributor. The effect of this rule is to stifle price competition.

Because of this rule, Valve can stop competing game stores from offering consumers a lower price on Steam-enabled games in order to shift volume from the Steam Store to their storefronts. Even if a rival game store were to charge game publishers a lower commission than Valve’s high 30% fee, the distributor would not gain more sales because the game publishers could not charge a lower price in its store. Game publishers and consumers suffer because this rule keeps Valve’s high 30% commission from being subject to competitive pressure.

This Price Parity Provision is one of the reasons why Valve has been able to continue to charge an inflated 30% commission for many years, even as that commission is plainly above the levels that would prevail in a competitive market. Competition would normally force such an inflated commission to come down to competitive levels—but Valve’s restraints prevent those competitive forces from operating as they would in a free market.

Because of Valve’s restraint, publishers cannot utilize alternative distributors to avoid the 30% tax that Valve has set for the market. Thus, they reluctantly market their games primarily through the dominant Steam Store where Valve takes its 30% fee. While several distributors have tried to compete with Valve by charging lower commissions on Steam Keys, those efforts have largely failed to make a dent in the Steam Store’s market share because publishers using those distributors had to charge the same inflated prices they set on the Steam Store.

Moreover, even if a game publisher wanted to scale up its use of Steam Keys to promote competition, Valve has made it clear that it would shut down such efforts. When Valve recognizes that a game publisher is selling a significant volume of Steam Keys relative to its Steam Store sales, Valve can, at its own discretion, threaten the game publisher and refuse to provide more Steam Keys. Thus, Valve uses the Steam Key program as another tool to ensure that the vast majority of sales take place on the Steam Store, where Valve gets its 30% commission on nearly every sale.

So if you want to sell steam keys, you need to offer a similar deal on steam as you would wherever you're selling those steam keys. This doesn't apply to other storefronts like GOG, Epic, the Ubisoft store, the EA store or the Windows store, this is only about selling steam keys. So if you want to avoid giving Valve a cut of the sale while still using their platform to distribute your game, Valve is going to get upset and take action to prevent you from doing that.

There is also a section about

Price Veto Provision. Valve also requires game publishers to agree to give Valve veto power over their pricing in the Steam Store and across the market generally (the “Price Veto Provision”). Valve selectively enforces this provision to review pricing by game publishers on PC Desktop Games that have nothing to do with the Steam Gaming Platform at all. Through this conduct, prices set in the Steam Store serve as a benchmark that leads to inflated prices for virtually all PC Desktop Games.

which I think was the focus of a different lawsuit that mostly talked about a Most Favored Nation clause. This one is a little more complicated, but this lawsuit ended up getting dismissed. I'm not even close to being a lawyer so I don't know why exactly, but this video seems to make a pretty good argument for why this isn't a good legal argument. To summarize: there isn't actually any proof that this kind of clause is actually anti-competitive and violates anti-trust laws. There's also no telling whether or not other storefronts have similar conditions in place, because apparently these kind of Most Favored Nation clauses are fairly standard in some industries.

Also being realistic if Valve were to drop their cut to 20% game prices wouldn’t change, the publishers would just pocket the difference, as we have seen with Epic.

You can’t point to current publisher behavior on EGS, because their behavior at present is influenced by Valve’s price policy (called the “Platform Most Favored Nation” or “PMFN” clause in the court filing) which is the foundation of the anti-competitive case against Valve.

Looking at your other comment, I can say that Ubisoft tried ditching steam, but their prices didn't really change even though they were paying a lower commission to epic than they would have to valve. So they would have had the ability change their prices to whatever they wanted on the epic store without fear of valve vetoing the price, because those games weren't being sold on steam.

Steam clearly wins on features, the only metric to beat them on is price. Epic is trying to do so, but publishers are not actually lowering the cost on their platform because of Valve’s policies—policies which are only effective because a publisher cannot afford to be delisted from Steam due its large market share.

Is there any actual proof of this? Epic is well known for giving games away for free, the best price customers can hope for. Yet they still can't seem to retain a loyal customer base. Maybe the price isn't the most important factor for a digital distribution platform.