Old thread, but putting this here for future searchers...
At least on my 2020 Specialized Roubaix to reconnect the Shimano Di2 to the battery, you just need to fish the cable out of your seat tube. The only tool I needed was a long pair of needlenose pliers.
There should be enough wire to bring it out geently about +- 1.5cm.
Next, remove the rubber plug at the end of the seat tube and put it on the wire that connects to your bike so you can replace it after you reconnect.
Finally, carefully grab the battery by the connector with a long needlenose and gently pull it to the end of the seat tube.
There is a plastic retainer clip that might come off, you can set that aside and replace it once you reconnect as it has a slit that can slide over the wire.

You can then re-connect it simply by your fingers, and there will be a slight but satisfying snap. Replace the retainer clip, rubber plug, apply fiber grip to the post, and gently slide the seatpost down the tube taking care not to pinch the wire in between tube and post. Make sure to test before making things permanent. Tighten clamp, And you're off!