In case it wasn’t clear, in “Additional CSS Classes”, the only thing to enter is “home-menu” (without quotes) – not the whole code snippet.
Instead of “home-menu”, you could use any name you want for the class. Let’s say you called it “example” instead. In that case, the CSS code for the static home page would be:
.home .wp-block-navigation-item.example.wp-block-navigation-link,
.wp-block-navigation-item.current-menu-item.wp-block-navigation-link {
color: #365ABA !important;
}
I checked your site, and if I understand the Inspector info correctly, you might have pasted in the whole bit of code.
Be sure you add the Additional CSS class to ONLY the page that’s chosen as your static home page in Settings > Reading Settings.
You add the custom class to that page’s link in the Navigation editor (not to the page in the Page/Post Editor).
Here’s a step-by-step, just in case:
Go to the Site Editor and click on Navigation (I like to select it in List View). You might have to open the Header to see “Navigation.” Then click on the little chevron icon to the left of the word “Navigation” to open the list of pages in the menu. (On my site, it takes a few seconds for the chevron icon to appear.) Then click on the page you’re using as the static home page, and add the Additional CSS class in the right column.
If none of this works, I’m not sure where to look next – I only know a little HTML and CSS! If you made any edits to style.css, un-do them if you haven’t already.
Does this help?