They seem to have the api base url hardcoded in their firmware[1]. The repo seems to have pretty clear instructions for compiling and flashing modified firmware. From there, it's just a matter of writing a decent server to implement the calls documented in BYOD/S[2] and Private API.[3]
[1]: https://github.com/usetrmnl/firmware/blob/e3db8c37990c2333ec...
[2]: https://docs.usetrmnl.com/go/diy/byod-s
[3]: https://docs.usetrmnl.com/go/private-api/introduction