I wonder if there is a way to view the list of the questions that were the most recently reopened on a given SE site.
There's an overview in the moderator tools - you need 10k reputation to access those, not a diamond:
Other than that, your best bet is probably SEDE: this query lists the most recently reopened questions since the last refresh (every Sunday morning UTC).
There is no way to get real-time information via a Stack Exchange API call - post history isn't exposed this way.
You can use the "Recently Reopened" list in the 10k tools (https://meta.stackexchange.com/tools?tab=Close&daterange=last30days), otherwise you're stuck with guessing using the homepage (reopens bump the question) or SEDE (only updated on Sundays).