Yep, your Google Search Console connection is working now as shown by the 200 status, so that part is correctly configured.
Eggy SEO Autopilot does help Google discover your content by automatically submitting your sitemaps to Google Search Console. It also monitors your tracked URLs through the Google URL Inspection API. Google does not provide an API that lets add ons simply force normal pages into the index, so sitemap submission and making sure Google can properly crawl the pages is the correct approach. Indexing itself is still ultimately decided by Google.
Your screenshots show 595 tracked pages and automatic sitemap submission is enabled, so you already have the main Google side configured correctly.
IndexNow is slightly different. Eggy SEO Autopilot already includes its own IndexNow integration and queue, which is what you can see under Sitemap / IndexNow with 9 URLs currently pending. IndexNow sends changed URLs to search engines that support the IndexNow protocol. Google currently does not use IndexNow, so it does not replace the Google Search Console integration.
Because SEO Autopilot already handles IndexNow itself, you should not need the separate IndexNow add on as well. Running both would potentially just result in the same URLs being submitted twice, so I would recommend using the SEO Autopilot implementation and disabling the separate add on once you have confirmed the queue is submitting successfully.
The blank Google API key shown in your other screenshot is only used for PageSpeed and CrUX performance data, so it is not required for your Search Console connection or sitemap submissions.
From the screenshots you have sent, your setup now looks substantially correct.