A summary for those who don't want to read the entire thing:
This case was originally granted back in 2019. It was scheduled for oral argument in March 2020, but was postponed at the last moment until October because of the pandemic. Being postponed at the last moment, it was fully briefed well over a year ago, and the justices likely knew how they would rule in the case for a long time. (It's unclear how much of an impact oral argument actually has on influencing the decisions). That it took so long for a decision to come out--this is the last October hearing to get an opinion--strongly suggested to me that this would be a messy case with several overlapping concurring and dissenting briefs.
It is not. It is a simple 6-2 decision, with a single majority opinion and a single dissenting opinion. I'm reading between the lines here, but it seems pretty clear that Breyer (the majority opinion author) does not believe that APIs are copyrightable in the first place, but doesn't argue that point as he probably does not have enough other votes to agree with him. It's plausible that Breyer had a lengthy section on why APIs weren't copyrightable but that was pulled due to the other justices in the majority rejecting it. We can't know what the voting would break down as, but a 3-3-2 breakdown of "API is uncopyrightable; API is copyrightable, but this is fair use; API is copyrightable, this is not fair use" does not strike me as implausible. (There's not much in favor of this breakdown, note: that I lay it out like this is as much wishful thinking as anything else).
Thomas's dissent--I'll focus on that first--essentially makes two main arguments. The first is that API is copyrightable in its own right (Breyer's opinion assumes that it is for the fair use analysis but doesn't say that it is). The second argument is that Google's copying of the API cannot be fair use. A lot of that argument appears back-reasoned from "Google copied so much of the API and they made so much money off of it, how can it possibly be fair." In a broader sense, however, it's a different mode of fair use analysis than Breyer argues for. Thomas essentially views copyright as a property interest, and fair use is a narrow limitation on property interest. The API is an entity in and of itself here, so even though the API is a tiny fraction of both the original and reimplementing code, you need to look at the amount of the API itself that is being copied to judge how substantial a portion it is. Although when he turns to consider the impact that an independent implementation has on the market for the original, it's not the market of the API itself that matters but the market of the entire implementation.
Now going back to Breyer's opinion, he treats fair use rather differently. First, Breyer essentially invokes the idea that different kinds of copyrighted material deserve different amounts of protection. He draws a distinction between declaring and implementing code, and notes that since only declaring code is being copied, it pushes the factor analysis much more towards being fair use than otherwise. In contrast to Thomas, Breyer notes that commercial use isn't automatically non-fair use, and lists a few examples of where commercial use can indeed be fair use. Also, Breyer pushes hard against the idea of copyright being about property interests, noting that the Constitution expressly provides that copyright is for the progress of science and arts. Whereas Thomas places primacy on the importance of the effect of the market, Breyer instead contends that it's the least important factor here.
All the way back at oral argument, Thomas surprised me with the most insightful question: the fair use factors in the law are very explicitly a nonexhaustive list, so what other factors might exist to sway fair use analysis? At opinion time, Thomas is instead the one to declare that none other exist, while it's Breyer who rather strenuously comments that fair use analysis is not exhaustive, although he does not include any other factors in his analysis.
What's the overall impact, then? APIs may or may not be copyrightable--SCOTUS does not decide. But Breyer essentially suggests that APIs have at best "thin copyright"--a lot of their use may be inherently fair use (the same analysis Breyer does here can reasonably be copy-pasted for a lot of API reimplementation cases). What's more radical is the effect it has on fair use analysis. Breyer states that appeal courts have to reconsider fair use on appeals if juries find a use to be fair or not (that's an easy part of the opinion to miss). Breyer upends the traditional notion of how to balance fair use factors yet again. Essentially, he suggests that the analysis of fair use is dependent in large part on what kind of work is being copied, and the balancing is dependent on the kind of work. He also rejects a lot of the traditional emphasis on market or potential market analysis for fair use. This is somewhat disclaimed for wider application to non-code cases, but you can bet there is now going to be a lot of appeals surrounding fair use over the next few years.