Search Console is Google's free report on your site's search life: which queries show you, what gets clicked, what's indexed, and what's broken. It's not analytics (that's GA4, about visitors on the site). It's the view from inside Google.
Yes, you need it. It's free, takes ten minutes to verify, and it's the only place Google tells you about problems directly: indexing failures, mobile issues, manual penalties, security flags. Running a site without it is running deaf.
The owner's monthly three minutes: Performance (queries trending up or down), Coverage (anything red), and, after site changes, a sitemap resubmit. Everything else can wait for a specific question.