I have one of these (picked it up secondhand), and as soon as I discovered the feature I set the BIOS feature which limits the battery charge to 50% to prolong its life.  I did this knowing that a battery replacement was very unlikely to be cost-effective.

This guide https://www.ifixit.com/Guide/Microsoft+Surface+Pro+4+Battery+Replacement/60358 suggests DIY replacement is possible, but not for the faint of heart.

You can log a support ticket with Microsoft to ask them for a quote.  Perhaps try this link?  https://account.microsoft.com/devices/select-device-for-repair  Anticipate the possibility your device would simply be traded for a refurbished one, so back up your stuff first.

Wow, the iFixit guide says two hours! That's a super long time to replace the battery!