It appears you're not alone in tearing the grip sensor cable when removing the battery. If you check out the Google Pixel 3 XL Teardown, you'll see they did the exact same thing when they were pulling the battery. It's too bad there's no repair guide for the 3 XL's grip sensors; maybe if you tackle the job you could document the process and contribute a guide!
The good news here is that replacement grip sensors are available on eBay for about $20 for a pair (left and right). I found two right off the bat using the search string "pixel 3 xl grip sensor".
Finally, to help things along, there does exist a guide on the Pixel 4 for replacing the grip sensor: Google Pixel 4 Left Grip Sensor Replacement. From that guide it appears the grip sensor is simply glued to the side of the housing; no soldering required.
The good news is it appears there isn't much, if any, further disassembly required to get to the grip sensor once the battery is out, unlike the Pixel 4 which seems to require a lot more part removal to get to it. I can't be sure, of course, but as best I can tell from the teardown photos it looks like the most you might need to do is to remove the speaker, for which there is a guide available.
Basically, if you read through the Pixel 4 grip sensor guide and follow along the last few steps, I think you may be in good shape with replacing yours.
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