Can the app edit blog posts I wrote myself in Shopify? (Essential AI SEO: AI Blog Post app)

No. The app only shows and edits posts that were created with it. Posts you wrote yourself in Shopify stay as they are, and you keep editing them in Shopify under Content → Blog posts.

To improve one of your own posts with the app, generate a new post on the same topic, then compare the two and keep the one you prefer.