feat(integration): add search engine creation

[manuel-rw]

Homarr

Thank you for your contribution. Please ensure that your pull request meets the following pull request:

• Builds without warnings or errors (pnpm buid, autofix with pnpm format:fix)
• Pull request targets dev branch
• Commits follow the conventional commits guideline
• No shorthand variable names are used (eg. x, y, i or any abbrevation)

[deepsource-io]

Here's the code health analysis summary for commits 56b57ad..6d7e1b3. View details on DeepSource ↗.

Analysis Summary

Analyzer	Status	Summary	Link
JavaScript	✅ Success		View Check ↗

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[github-actions]

Coverage Report

Status	Category	Percentage	Covered / Total
🔵	Lines	21.57%	7934 / 36774
🔵	Statements	21.57%	7934 / 36774
🔵	Functions	24.76%	287 / 1159
🔵	Branches	61.8%	864 / 1398

File Coverage

File	Stmts	Branches	Functions	Lines	Uncovered Lines
Changed Files
apps/nextjs/src/app/[locale]/manage/integrations/new/_integration-new-form.tsx	0%	0%	0%	0%	1-169
packages/api/src/router/integration/integration-router.ts	54.92%	82.35%	100%	54.92%	77-122, 127-131, 149-153, 221-225, 279-283, 288-356, 361-377, 382-398, 404-405, 444-456
packages/db/schema/mysql.ts	100%	100%	100%	100%
packages/db/schema/sqlite.ts	100%	100%	100%	100%
packages/icons/index.ts	100%	100%	100%	100%
packages/icons/src/auto-icon-searcher.ts	33.33%	100%	0%	33.33%	6-9
packages/validation/src/integration.ts	100%	100%	100%	100%

Generated in workflow #4428 for commit 6d7e1b3 by the Vitest Coverage Report Action