azure-devops-auth-samples | Samples showing how to auth with Azure DevOps | Azure library

I understand that I have to register and run a whole web application. Am I understanding this correctly ? I there a simpler way ?

Yes, you are right. You have to register whole web application.

As the interface in Postman for OAuth2, we need provide the CallbackUrl, ClientID, ClientSecret and so on. Then, we check the document Requesting an OAuth 2.0 token, we could to know the Callback URL is:

The client application callback URL redirected to after auth, and that should be registered with the API provider.

So, we have to register an OAuth client app in Azure DevOps (https://app.vsaex.visualstudio.com/app/register), then we could get the following information, like:

You could check the document Authorize access to VSTS REST APIs with OAuth 2.0 for some more details.

AFAIK, there is currently no simpler way to get a bearer token to send requests to the Azure DevOps API.

Hope this helps.