Fixes https://github.com/zed-industries/zed/issues/13073

Note that, contrary to the issue's text, we're still shipping a
statically bundled sqlite3 after this PR. We use enough new features of
sqlite, like `sqlite3_error_offset` and `STRICT`, that our minimum
version (v3.38.0) is higher than is presumably accessible on Ubuntu.

Release Notes:

- N/A

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Co-authored-by: Mikayla <mikayla@zed.dev>