We should add an icon to indicate what is currently set as the home template:

The order should reflect some hierarchy as well, with home page / front page being always at the top.
And also need to start thinking about the site setting and how it interacts with the blog being set as home or on a sub-path.
Does this need to be reflected here or in something like a template manager? I could also envision a Template "tab" next to Document and Blocks in the sidebar that displays information about the template like theme, pages using it, template parts.
We need something like that, but wouldn't a home icon in the template switcher also be a good addition?
Here's a mockup by @joanrho that does the job:

Some questions:
For now, I think it's definitely a good start.
SVG code:
<svg width="10" height="10" viewBox="0 0 10 10" fill="none" xmlns="http://www.w3.org/2000/svg">
<path d="M9.5 4V9.5H6.75V6.25V5.75H6.25H3.75H3.25V6.25V9.5H0.5V4L5 0.625L9.5 4Z" fill="black" stroke="black"/>
</svg>
Yes, a tooltip on the icon would suffice, right?
A tooltip with text along the lines of "Current Home page template" could be helpful since the template name could be anything. Or, would it communicate better if it were a line of text at the very top of the Template Preview pane, since that preview appears alongside each template on hover over template name?
Yes, a tooltip on the icon would suffice, right?
Totally. As long as it plays nicely with the menu.
"Current Home page template"
Right! Perhaps a slightly shorter version: "Home page template"
@MichaelArestad See #22004
Commented on the PR, but we should not introduce another baseline icon grid of 10/10.