Same issue here. Surface Pro 4 - 256GB i7 16GB. Battery bulged so bad it pushed the front LCD screen off and caused a gap. The unit was purchased in 2015 (five years ago) so no longer under any kind of warranty. The unit still worked, despite the threat of the battery burning up or exploding.
Microsoft agreed to replace with a refurb for US $478.13 which seemed reasonable considering the original cost without dock and type cover was $1,799.00. Does it have new batteries in it? I would hope so! Who knows? But if I can get another five years out of it that would be great.
The way it went was first I had to provide a photo of the bulge to MS support, then I paid with credit card for the new machine and they shipped a special fire-resistant box with postage for UPS. I packed up the damaged unit and shipped it to them and once they received it and inspected, then sent me a new unit.
Before shipping the old one, I did a clone of the entire drive (multiple partitions) using Clonezilla, then restored it all to the new machine when it arrived. Works just like the old. Fairly happy with that solution. We always take a risk when buying a one-piece tablet as opposed to something accessible and upgradable.