Connecting to server and Cloud instances of Jira with Python is accomplished with much the same method and approach. The only differences between the two are that Server uses a username and password, while Cloud uses a username and token.

Generating a token is pretty straightfoward.  I recommend reading the documentation first.

The script below consists of essentially three pieces.   You define the connection parameters,  create the headers used to authenticate against the instance, and return the results of the authentication request.

The script example below returns one page of project results from each instance, just to demonstrate how it works.  If you wanted to actually work with the results, they’d need to be converted to JSON or some other format. 

The process for connecting to Confluence is the same; you need only point the script at a Confluence instance (and switch to returning some Space data or something).

import requests
import base64

server_username = "<username>"
server_password = "<password>"
server_url = "<url>"
#Define connection parameters for the server side

cloud_username = "<Cloud login email>"
cloud_token = "<Cloud token"
cloud_url = "<Cloud url>"
#Define connection parameters for the Cloud side

server_credentials_string = f'{server_username}:{server_password}'
server_input_bytes = server_credentials_string.encode('utf-8')
server_encoded_bytes = base64.b64encode(server_input_bytes)
server_encoded_string = server_encoded_bytes.decode('utf-8')
#Encode the server credentials

cloud_credentials_string = f'{cloud_username}:{cloud_token}'
cloud_input_bytes = cloud_credentials_string.encode('utf-8')
cloud_encoded_bytes = base64.b64encode(cloud_input_bytes)
cloud_encoded_string = cloud_encoded_bytes.decode('utf-8')
#Encode the Cloud credentials

server_headers = {
    'Authorization': f'Basic {server_encoded_string}',
    'Content-Type': 'application/json',
    'Accept': 'application/json',
}
#Define the headers used to connect to the server

cloud_headers = {
    'Authorization': f'Basic {cloud_encoded_string}',
    'Content-Type': 'application/json',
    'Accept': 'application/json',
}
#Define the headers used to connect to the Cloud

server_login_request = requests.get(f'{server_url}/rest/api/2/project', headers=server_headers)
cloud_login_request = requests.get(f'{cloud_url}/rest/api/2/project', headers=cloud_headers)
#Initiate the connection requests to the server and cloud instances

print(f"Server connection HTTP status: {server_login_request.status_code}")
print(f"Cloud connection HTTP status: {cloud_login_request.status_code}")

print(f"Server response content: \n{server_login_request.content}")
print(f"Cloud response content: \n{cloud_login_request.content}")
#Print some data to confirm successful connection