Google claims that "browsers" support an API if it's supported in Chrome and in Microsoft Edge, a Chromium-based browser.
I think that's a fair claim, because MS does sometimes block Chromium features that they don't like. https://www.techradar.com/news/microsoft-edge-becomes-latest...
Microsoft could have blocked File System Access, for some of the same reasons that Mozilla did, but they didn't; they elected to enable the feature.
Since Microsoft + Google together have 70% share of desktop web, and since Microsoft agrees with Google that the File System Access API is a good thing for the web, I think it's not wrong to say that "browsers" support this feature.
Now, you might say, "Microsoft shouldn't count!" but Edge's market share is bigger than Firefox, and we all agree that Mozilla's vote should count (at least as long as they can hang on to 3% market share).