I’ve changed the Open Graph URL in the home page and I still can’t figure out how to change the image that pops up when searching the website. I noticed that when searching the website on Google and Safari, different icons appear on both that come from my website’s home page.
og:image and twitter:image is for social sharing and works for those platforms when you share the link directly. It’s not meant to work for search results.
You need to add the structured data for Logo to your page to make it work for Google’s index.
Here’s the documentation on how to do that.