MRT - Taoyuan HSR Station to Taoyuan Airport via MRT

I seem to recall being able to take the train directly from the Taoyuan HSR station to Taoyuan airport, albeit having to cross the street at that Outlet mall, yet Google maps is telling me the only option is taking a train plus 55 minutes of walking, and googling says i need to wait for a bus that comes every 40-60 minutes.

So is it still possible to take the HSR to Taoyuan station then take an MRT more or less from there to TPE (Taoyuan Airport)?

Also if so, does anyone know the cost?

30NTD to terminal 1


Thank you