That comparison is somewhat more complicated because it was much more broadly tied into Microsoft's control of the by-far dominant PC operating system and was in the era where browsers were commercial products which cost money and significantly predated the rise of open source software.
That's likely why the DOJ is _not_ “suing Apple for doing this”. Browsers are conspicuously not on the list of charges and I think it's because in the subsequent 3 decades, we've had some key changes: all of the major browser engines are open source, very few people question the demand for standard libraries for rendering web content even in desktop apps, statistically nobody pays for web browsers. A large part of the Microsoft trial was discussing how they colluded to prevent PC vendors from bundling other companies' software but in this case Apple isn't trying to restrict another vendor's decision about what software they ship on their hardware and users don't show much sign of being bothered by the lack of PWAs, which have negligible usage on any platform. If someone was making a lot of money with a PWA on Android but having to pay Apple's in-app fees on iOS, that'd be a much stronger argument for market distortion.
The actual lawsuits are focused where Apple's behavior is more clearly like 90s Microsofts: restricting access to the NFC APIs, restricting game streaming platforms, and restricting the ability of WearOS watches to work with iOS phones or Apple Watches working with Android phones. Unlike PWAs, there are other mobile payment companies who'd love to ship tighter integration, customers who want more gaming options, or who want to have something like a Garmin device as tightly integrated as an Apple Watch. I don't know how likely the DOJ's case is to succeed but at least in those cases it's easy to show that there's a real market being affected whereas it's much harder to argue that a PWA market would suddenly spring into being or that Google is somehow being deprived of Chrome revenue by having to use WebKit on iOS. I'm aware of the technical arguments but it seems fairly challenging as a legal argument to make the case that the DOJ should respond to Apple abusing a monopoly position with a fifth of the market by allowing Google to push their share over 90%. The only way the web is better off out of this is if there's some coordinated simultaneous action.