Just got my daughter a charge 4 so she didn't need to run with my phone. We have runkeeper connected to fitbit. Can you start a runkeeper run from the fitbit, does it show the route you took.
You don't need the phone to track a run with the Charge 4.
Let's see if we can see what runkeeper has chosen to pull from your Fitbit account. See this post but be aware that runkeeper is in charge of what syncs.