The unit test suite shows one case of improved "exception text". I'd say it's an improvement.

$ ./python.exe  # with GH-24586 applied
>>> import sqlite3
>>> c1 = sqlite3.connect(":memory:")
>>> c2 = sqlite3.connect(":memory:")
>>> c1.backup(c2, name="non-existing")
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
sqlite3.OperationalError: unknown database non-existing

$ python3.10  # latest alpha from python.org
>>> import sqlite3
>>> c1 = sqlite3.connect(":memory:")
>>> c2 = sqlite3.connect(":memory:")
>>> c1.backup(c2, name="non-existing")
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
sqlite3.OperationalError: SQL logic error