I had a look into the extension's source: It's stored inside web extensions `storage.local` area, as `[time]: { text }` objects. It also keeps both a time index (timestamp of all existing entries) and a two week "preloaded cache" for quick access, which means all visited sites from the past 14 days are permanently in your browser memory. This could theoretically lead to memory problems, as the websites' texts are never truncated. If you search for text older than that, all entries for the specified time frame (determined using the time index) are retrieved from storage (again, possibly large amount of memory) and then processed.

This is all pretty clever and a reasonable implementation imo. I'm not sure what better way there could be using web extensions (that support FTS) - the only thing I could think of is a WASM SQLite module.