Do I track everything

Your Fitbit already sees that extra activity is tracking it already.
Actually, probably underestimates a decent amount of non-moving based stuff, but maybe inflated on other bits.

It then reports to MFP your total amount burned so far.

MFP then corrects itself by way of an Adjustment listed under exercise as to how much you have burned or expected to.

MFP then removes a deficit to cause hopefully just fat loss.

You eat the stated goal.

So you manually track nothing - Fitbit is auto-tracking it all.

If you want to track workouts separately and Fitbit isn't auto-creating them, you can start an Activity Record for workouts.

On MFP, just make a wall post about the workout and what you did if you want friends list to see it.