Yoast SEO plugin is provided by the Yoast team which has been in this game for long. Yoast SEO plugin helps you to manage your SEO easily. This is one of the most popular plugins along with RankMath.
To be seen on Google you need to add your WordPress website to the Google Search Console. What this means is that you submit your website to Google and google bots start crawling on your website. The bots go through every possible link on your website and index your entire website as it stores it on Google servers.