I've been able to reproduce the issue on Firefox 115. I also noticed the add Shortcut Button can appear more than once. Refreshing the page does indeed fix the dupe Add Shortcut issue and the wrong tile title issue. It's worth noting the Top Sites listing in the address bar is as expected, so this could potentially be more of a New Tab specific implementation issue than an issue with Top Sites itself.
Bug 1894013 Comment 3 Edit History
Note: The actual edited comment in the bug view page will always show the original commenter’s name and original timestamp.
I've been able to reproduce the issue on Firefox 115. I also noticed the add Shortcut Button can appear more than once. And this doesn't just happen with default top sites, a custom added top site can cause the same issue. Refreshing the page does indeed fix the dupe Add Shortcut issue and the wrong tile title issue. It's worth noting the Top Sites listing in the address bar is as expected, so this could potentially be more of a New Tab specific implementation issue than an issue with Top Sites itself.