>>847340not really
sites can't interact with anything outside of the current tab, so they'd only be able to log keystrokes on the current page which isn't very useful since the main usecase for keylogging is stealing credentials (this is why online payment shit like paypal will open its open window)
they'd also need to send those recorded keystrokes back to the server which would be very easy to spot in the network tab of any browser's debug tools