Google, Apple, and Mozilla apparently all failed to find a solution to this problem, even though lots of people
wanted there to be a solution. Certainly, any browser that shipped this feature in a privacy-respecting manner would have bragging rights for awhile, so there is an incentive. Given that, I don't think I'm exaggerating the difficulty of the problem. This problem is also very similar to the challenges brought by Spectre-class vulnerabilities, and that one has been enormously costly for the whole industry.
I think it is completely fair to say that privacy-respecting shared caches are not simple.
Some solutions can be imagined, but they come with weird trade-offs or they do nothing for majority of the web. A new manifest format like you describe falls into the latter, since it would only apply to new websites using the new feature, and that’s without digging into the other problems it would pose.
In practice, people often visit the same websites repeatedly; they aren't constantly visiting new websites only once. A partitioned cache works just fine for the normal scenario. It's slightly less efficient for the first day someone uses their browser, but then things are honestly fine after that. It's unfortunate that we can't eek out the last tiny bit of performance for this, but I think the difference would be hard to measure in practice.
In my opinion, if websites would more commonly use brotli, that would make a far larger difference in efficiency than returning to a shared cache, and if browsers could have a standardized means of downloading only the bytes that changed in an asset like a javascript library instead of downloading the new version from scratch, that would make a much bigger difference too.