I had the same issue - Charge 2 but with the Pixel 3a, tried all the steps indicated and had the same results.
I FOUND A WORK AROUND reading through all sorts of guides online. Find another device - I used an old phone (an original Pixel) - and install the latest Fitbit app on it and set up the Charge 2 as a new device. I followed all the steps, but instead of failing at the 4-digit code it accepted the 4-digit code and then connected. It was then paired with my old phone and would sync beautifully.
I restarted my current phone (Pixel 3a) and the Fitbit app. I assume something in the Fitbit app did a sync to my account, because the Charge 2 suddenly appeared as a connected device. Another device also appeared, but I've since removed it without issue.
See if you can set it up on another device - be sure to use your same Fitbit account.
My sync initially stopped on Sept 27, 2020, and I performed all the above steps on October 10, 2020. I've been able to sync fine with my Pixel 3a since this. I turned off my old phone and it hasn't been on since.
HOWEVER, prior to Sept 27, I would easily get at least 5 days on a full battery charge. Since reconnecting, I have about 30-35% battery drain daily, which means I have to fully charge it every other day to avoid any 'low battery' notifications. When I open the Fitbit app, the stats are very up to date as if it is constantly connected, and I can't find any option in the app to prevent it from being constantly connected. Old version of the app had it, but I can't find it now. Coincidence, or related to the initial sync issue? I don't know yet.
