I don't have a good solution to your question. Microsoft itself has a recycling program, but they use a 3rd party vendor who does not take damaged batteries. It may not be safe to attempt to open the Surface Pro with a swollen battery as there is danger of puncturing. See https://support.microsoft.com/en-us/surface/battery/caring-for-your-surface-battery which says (in part) -
And these recycling drop off centers don't take damaged batteries.