In the mean time I came across this post (among others!) where users shared a photo of the PCB. My battery pretty much looks like the one also shared in that post. I might not have the right tools or skills to remove the PCB, but I'll give it a try as long as I'm comfortable messing with the swollen battery. As long as the MUDI works plugged to the power adapter without a battery connected, that's fine for my use case. The same post also mentions it will work with a power bank connected, if I need to. Nevertheless I'll follow your advise and pm you for more details.
Thanks everyone that has shared their knowledge about this issue. GL-Inet doesn't seem to deserve such a dedicated community.