Copy the link and place it in a Google doc/slide/sheets etc. and then hover over it there.
OK, so this is not even about previews of links in your own site, but previous of your website’s pages outside your site.
Unfortunately that’s entirely up to that external site/software, and not something 100% within your control.
Social media and messaging sites generally use the OpenGraph meta tags. WordPress does not add the tags, but your site uses the AIOSEO plugin for this.
Google Docs/Slide/Sheets uses the site’s icon (favicon) along with the page’s title and/or description to create these link previews (they called this “smart chips”).
Other sites/apps may use oEmbed where supported. Others may generate an actual screenshot of the destination page as the link preview.
Again, that’s entirely up to the external site/app.
It would be a native WP issue if I’m not allowed to change that anywhere on the backend when it’s pulling a random image for it.
That’s ultimately up to the external site/app, not WordPress or your website.
Specifically for Google, you can control this only to the extent that you can control the individual elements Googe claims to use (favicon, title & description). Oh, and it’s common knowledge that Google often displays totally random and unrelated icons for sites in their search results.