Finally!
Based on the above linked discussion, I was able to add
[experimental]
networkingMode=mirrored
to .wslconfig and that gave me IPv6 connectivity inside my WSL instance. I can now successfully run:
curl -6 https://<host>/latest.json?order=created
It still doesn’t work on my WiFi though and that’s very likely becuase this old router doesn’t support IPv6. It works fine when using my phone’s hotspot.
Thank you so much @JammyDodger for the pointers, you led me in the right direction!