To access Codecov's API as an authenticated user please create an access token in Codecov. To create an access token please follow these directions:

Navigate to your personal (not org) account page by clicking on your avatar (top right corner) then Settings
Click on Access on the left side menu
Click on Generate Token button
Type in a token name and click Generate
Use this token in your API requests as stated below.

You can supply the token as an Authorization header like below:

curl --location --request GET 'https://codecov.io/api/v2/{{ SERVICE NAME }}/{{ ORGANIZATION NAME }}/users' \
     --header 'Authorization: bearer {{ ACCESS TOKEN }}'