A good example is superhuman the email client. They cache data in the browsers local web sql database.https://en.wikipedia.org/wiki/Web_SQL_Database

Then all searches etc are fast, due to not having to go to the server.

I'm not sure how they implement that, but I would probably go with a websocket that sends the latest data to the client which then stores it in Indexed DB (the browsers local database).

I don't know of any solution that does this out of the box.