Let's create a decently complicated stacktrace, in order to demonstrate that we get the full stacktrace:

def raise_error():
    raise RuntimeError('something bad happened!')

def do_something_that_might_error():
    raise_error()

Logging the full stacktrace

A best practice is to have a logger set up for your module. It will know the name of the module and be able to change levels (among other attributes, such as handlers)

import logging
logging.basicConfig(level=logging.DEBUG)
logger = logging.getLogger(__name__)

And we can use this logger to get the error:

try:
    do_something_that_might_error()
except Exception as error:
    logger.exception(error)

Which logs:

ERROR:__main__:something bad happened!
Traceback (most recent call last):
  File "<stdin>", line 2, in <module>
  File "<stdin>", line 2, in do_something_that_might_error
  File "<stdin>", line 2, in raise_error
RuntimeError: something bad happened!

And so we get the same output as when we have an error:

>>> do_something_that_might_error()
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "<stdin>", line 2, in do_something_that_might_error
  File "<stdin>", line 2, in raise_error
RuntimeError: something bad happened!

Getting just the string

If you really just want the string, use the traceback.format_exc function instead, demonstrating logging the string here:

import traceback
try:
    do_something_that_might_error()
except Exception as error:
    just_the_string = traceback.format_exc()
    logger.debug(just_the_string)

Which logs:

DEBUG:__main__:Traceback (most recent call last):
  File "<stdin>", line 2, in <module>
  File "<stdin>", line 2, in do_something_that_might_error
  File "<stdin>", line 2, in raise_error
RuntimeError: something bad happened!

This approach of this answer is new since Python 3.10. This reusable function writes the exception and traceback into a string buffer, and from there as a string.

import io
import traceback


def get_exception_traceback_str(exc: Exception) -> str:
    # Ref: https://stackoverflow.com/a/76584117/
    file = io.StringIO()
    traceback.print_exception(exc, file=file)
    return file.getvalue().rstrip()

Sample usage:

try:
    assert False, 'testing assertion'
except Exception as exc:
    error = get_exception_traceback_str(exc)

print(error)

Sample output:

Traceback (most recent call last):
  File "<input>", line 2, in <module>
AssertionError: testing assertion

Note: To just print the exception and traceback instead, you don't need it in a string, so consider using just traceback.print_exception(exc).

Since Python 3.0^{[PEP 3109]} the built in class Exception has a __traceback__ attribute which contains a traceback object (with Python 3.2.3):

>>> try:
...     raise Exception()
... except Exception as e:
...     tb = e.__traceback__
...
>>> tb
<traceback object at 0x00000000022A9208>

The problem is that after Googling __traceback__ for a while I found only few articles but none of them describes whether or why you should (not) use __traceback__.

However, the Python 3 documentation for raise says that:

A traceback object is normally created automatically when an exception is raised and attached to it as the __traceback__ attribute, which is writable.

So I assume it's meant to be used.