So will this be the new recommended way to get into London from Heathrow?
Just another option, it really depends where you are going. My understanding is that the stretch from Heathrow to Paddington is not new, just the existing National Rail infrastructure "rebranded" to the "Elizabeth Line", from Paddington to Abbey Wood, (change required at Paddington) that is new, so modern stations, easy accessibility, but only preferred if that is where you need to go.
The Heathrow Express is more a separate train, not a route, I imagine they will continue on, offering fewer stops and a slightly faster trip, and for many the Piccadilly line will continue to be "Best" in that it is cheaper and gets you where you are going.