As others have noted there is a nice requests-toolbelt module with convenient functions to dump request and response content using requests hooks. Unfortunately (as of now) there is only a hook to be invoked on a successful completion of a request. It's not always a case. I.e. request could end up with ConnectionError or Timeout exceptions.
The requests-toolbelt module on it's own also provides public functions to dump completed requests only. However using a bit of non-public APIs and Session sub-classing it's possible to implement logging of requests before send and logging of responses after receive.
NOTE: code relies on implementation details/non-public APIs of requests-toolbelt module and thus make unexpectedly break in the future:
import requests
from requests_toolbelt.utils import dump
class MySession(requests.Session):
    def send(self, req, *args, **kwargs):
        prefixes = dump.PrefixSettings(b'< ', b'> ')
        data = bytearray()
        try:
            dump._dump_request_data(req, prefixes, data)
            resp = super().send(req, *args, **kwargs)
            dump._dump_response_data(resp, prefixes, data)
        finally:
            print(data.decode('utf-8'))
        return resp
and here is an example of usage:
>>> MySession().get('https://httpbin.org/headers')
< GET /headers HTTP/1.1
< Host: httpbin.org
< User-Agent: python-requests/2.25.1
< Accept-Encoding: gzip, deflate
< Accept: */*
< Connection: keep-alive
< 
> HTTP/1.1 200 OK
> Date: Fri, 19 Aug 2022 10:43:51 GMT
> Content-Type: application/json
> Content-Length: 225
> Connection: keep-alive
> Server: gunicorn/19.9.0
> Access-Control-Allow-Origin: *
> Access-Control-Allow-Credentials: true
> 
{
  "headers": {
    "Accept": "*/*", 
    "Accept-Encoding": "gzip, deflate", 
    "Host": "httpbin.org", 
    "User-Agent": "python-requests/2.25.1"
  }
}
>>> MySession().get('https://non.existent')
< GET / HTTP/1.1
< Host: non.existent
< User-Agent: python-requests/2.25.1
< Accept-Encoding: gzip, deflate
< Accept: */*
< Connection: keep-alive
< 
Traceback (most recent call last):
  File "/usr/lib/python3/dist-packages/urllib3/connection.py", line 169, in _new_conn
    conn = connection.create_connection(
  File "/usr/lib/python3/dist-packages/urllib3/util/connection.py", line 73, in create_connection
    for res in socket.getaddrinfo(host, port, family, socket.SOCK_STREAM):
  File "/usr/lib/python3.10/socket.py", line 955, in getaddrinfo
    for res in _socket.getaddrinfo(host, port, family, type, proto, flags):
socket.gaierror: [Errno -2] Name or service not known
...