I can try to clarify a few things here.
First, make sure you are using the most recent collection:
https://postman.meraki.com/
The API key is applied via the "Temporary Headers", meaning you do not have to specifically write X-Cisco-Meraki-API-Key in your request header section.
The Demo API key 093b24e85df15a3e66f1fc359f4c48493eaa1b73 should certainly work for this initial call `{{baseUrl}}/organizations`.
Your environment will still need the X-Cisco-Meraki-API-Key defined, as you have done. Just be sure you are using the API key you have intended (initial vs current). This can be verified after you run the request as well (see image)
If you are curious how this works, edit the Meraki Dashboard API collection and view the Authorization tab.
The Variables section is a list of all the global properties that could be overwritten within your personal environment. It also contains a few defaults, such as the baseUrl.
If nothing is working for you, then try from another network to rule out any security issues.