Example to show the callout after DML rollback in Apex with new Database.releaseSavepoint

SavePointReleaseCalloutExample.cls

// This class works if your class -meta.xml is of 60.0 version
public with sharing class SavePointReleaseCalloutExample {

    public void basicAuthCallout() {
        
           // Do a DML before callout
            Savepoint sp = Database.setSavepoint();
            
            Account acc = new Account();
            acc.Name = 'Test';
            insert acc;
            
            Database.rollback(sp);
            
            Database.releaseSavepoint(sp);

            HttpRequest request = new HttpRequest();
            request.setEndpoint('https://dog.ceo/api/breeds/image/random'); // Set the endpoint URL
            request.setMethod('GET'); // Set the HTTP POST method
        
            // Set the request headers
            request.setHeader('Content-Type', 'application/json');
            request.setHeader('Accept', 'application/json');
        
            // Send the request
            Http http = new Http();
            HttpResponse response = http.send(request);
        
            // Process the response
            if (response.getStatusCode() == 200) { 
                String responseBody = response.getBody();
                System.debug(responseBody);
            }
    }
}

Please note that if the Account Trigger does a DML-ish operation (eg. sending a mail or scheduling a batch), then the Http request will still throw a CalloutException even if the transaction is rollbacked and Database.releaseSavepoint(sp); is called.

About the dml-ish thing (made-up term) : https://salesforce.stackexchange.com/a/240041

Some operations are "DML-ish", meaning they persist something to the database to be committed at the end of the transaction, just not a standard DML operation on an sObject. Enqueuing Batch Apex, for example, is a DML-ish operation. [...] Because this is persisting something (the email send attempt) until the transaction commits, it has the same effect on later callouts as regular DML - that is, it blocks them due to the uncommitted work that's in flight.

About releaseSavepoint being uneffective : https://developer.salesforce.com/docs/atlas.en-us.apexcode.meta/apexcode/langCon_apex_transaction_control.htm

If there’s uncommitted work pending when Database.releaseSavepoint() is called, the uncommitted work isn’t rolled back. It’s committed if the transaction succeeds.