Your business website should be monitored for SEO purposes if you rely on traffic for your business from search engines like Google. Else, not a requirement.
In the case, if you want to outrank your business rival for a higher ranking in the search engines, you may monitor by keeping an eye on their websites for research and analysis so that you can grasp their content, keywords, and other information based on your business goals.
It all depends upon your specific objectives and varies from business to business.
You may make use of globally recognized SEO Tools such as Ahrefs and Semrush for detailed monitoring for SEO purposes.
If interested, you may also access this SEO Maintenance Checklist.
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