Update the SQLite database plugin to v2.2.13 to support any DB_NAME and fix preview sites

[sejas]

Related issues

• Part of STU-799
• Dynamic database name WordPress/sqlite-database-integration#266

Proposed Changes

• Update SQLite integration plugin, so it works for any DB_NAME

Testing Instructions

• Apply this branch and run npm i && npm start
• Create a new site
• Edit wp-config.php and set define( 'DB_NAME', 'antyhing_here' );
• Confirm the site works as expected
• Restart the site
• Confirm the site is still working
• Test other features to confirm there are no regressions, such as exporting the database or importing a backup.

Pre-merge Checklist

• Have you checked for TypeScript, React or other console errors?

[github-actions]

📊 Performance Test Results

Comparing b7ae944 vs trunk

site-editor

Metric	trunk	b7ae944	Diff	Change
load	8399.00 ms	12123.00 ms	+3724.00 ms	🔴 44.3%

site-startup

Metric	trunk	b7ae944	Diff	Change
siteCreation	22255.00 ms	21330.00 ms	-925.00 ms	🟢 -4.2%
siteStartup	6969.00 ms	5984.00 ms	-985.00 ms	🟢 -14.1%

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Results are median values from multiple test runs.

Legend: 🟢 Improvement (faster) | 🔴 Regression (slower) | ⚪ No change

[wojtekn]

A site with an incorrect database name now functions properly.

Other use cases like adding a site, importing, exporting work,too.