Your "Old API" is pointing at a specific shard nxxx, I don't think referencing a shard has ever been advocated as the base URI (other than as a workaround for some problems a while ago), it generally works, but it's not the proper way.
In most parts of the world, every API request should begin with the following base URI:
https://api.meraki.com/api/v1
...this has been the standard for many years now.
The recent change is that for organizations hosted in the following dashboards, you need to specify the respective base URI instead:
Dasboard/Country URI
What failure code(s) are you getting?