Default mypy configuration crashes on python build without sqlite

Crash Report

Since PR #21041 the sqlite cache is used by default.
This however fails when python was build without sqlite3 support and causes mypy to report an INTERNAL ERROR..

Traceback

• v1.20.1

Traceback (most recent call last):
  File ".../site-packages/mypy/__main__.py", line 15, in console_entry
    main()
  File "mypy/main.py", line 141, in main
  File "mypy/main.py", line 231, in run_build
  File "mypy/build.py", line 388, in build
  File "mypy/build.py", line 462, in build_inner
  File "mypy/build.py", line 877, in __init__
  File "mypy/build.py", line 1619, in create_metastore
  File "mypy/metastore.py", line 181, in __init__
  File "mypy/metastore.py", line 158, in connect_db
  File ".../sqlite3/__init__.py", line 57, in <module>
    from sqlite3.dbapi2 import *
  File ".../sqlite3/dbapi2.py", line 27, in <module>
    from _sqlite3 import *
ModuleNotFoundError: No module named '_sqlite3'

• v2.0.0:

Traceback (most recent call last):
  File ".../site-packages/mypy/__main__.py", line 16, in console_entry
    main()
  File "mypy/main.py", line 154, in main
  File "mypy/main.py", line 244, in run_build
  File "mypy/build.py", line 385, in build
  File "mypy/build.py", line 1911, in create_metastore
  File "mypy/metastore.py", line 200, in __init__
  File "mypy/metastore.py", line 166, in connect_db
  File ".../sqlite3/__init__.py", line 57, in <module>
    from sqlite3.dbapi2 import *
  File ".../sqlite3/dbapi2.py", line 27, in <module>
    from _sqlite3 import *
ModuleNotFoundError: No module named '_sqlite3'

To Reproduce

Build a python when the sqlite libraries are not installed.

Your Environment

• Mypy version used: 1.20.2 (and also tested on 2.0.0)
• Python versions: 3.10, 3.11 (later untested)

Work-arounds

• Run with: mypy --no-sqlite-cache
• Update pyproject.toml:

 [tool.mypy]
sqlite_cache = false

• Update mypy.ini:

[mypy]
sqlite_cache=false

Start with mypy/metastore.py, especially connect_db, and trace how mypy/build.py creates the metastore. Reproduce the failure using a Python build without sqlite3 support while the default SQLite cache is enabled, then inspect the documented --no-sqlite-cache and configuration settings. Done means mypy no longer raises an INTERNAL ERROR in that environment and the relevant behavior is covered by a test.