From my poking around the dark corners of the internet, it appears that orange cable is part of the battery itself. I saw no indication at all that the cable can be purchased by itself, and there were no pictures showing how it connects to the battery, as it goes under a glued-on cover before making connection.
So really, the only hope here is that if you uncover the connection and find that it's some sort of plug connector, then you could probably replace it, assuming you can locate that flex cable. I had zero luck finding it, so to be honest I strongly suspect you're going to have to replace the battery to recover from that particular mistake. Here's the iFixit guide showing you how to replace the battery.
[guide|161057|Google Pixelbook Go Battery Replacement - iFixit Repair Guide|new_window=true]
Unfortunately, the batteries on that Chromebook aren't cheap; most of them I saw were running right around the $100 USD range, making this a somewhat expensive error, sorry to say. Here's a typical example; you may be able to find something cheaper with an extensive search on places like Amazon, eBay or AliExpress.
[link|https://www.ebay.com/itm/353974355093|USA 100% new Genuine 7.64V 47.4Wh B50 battery For Google Pixelbook Go 13.3" - eBay|new_window=true]