Some noise is common as these things wear. I wonder if you're running into the flip side of this: https://www.sheldonbrown.com/chain-life.html I.E., getting the worst of all worlds when the new chain meshes on a cog and chainring that are worn on every other tooth.

If it were my bike, I'd just run it and try to tune out the noise while the new chain wears in. Replacing the whole drivetrain each time is an option to keep everything smooth, but I wouldn't want to replace expensive chainrings and cogs every time a $15 chain wore out.