There’s a lot of confusion about what the Chrome extension storage APIs do, in part because of confusing and out of date docs. I wouldn’t be surprised if this was just due to a misunderstanding... curious if @slightlylate or others know though?
My recollection is that it’s generally thought the extensions permissions would give you more storage (as the string “unlimited storage”) would suggest, but in fact it was persistence they affected, not quota. This area is mighty confusing though....
AFAIK the web platform still doesn't have filesystem APIs and IndexedDB file storage requires some rather unfortunate workarounds like splitting a large file into multiple blobs for storage and reassmebling them on read
I may well be mistaken/out of date, though