Ok, long story short:
MS Excel on macOS has a list of recently used files. This list holds up to 25 entries and keeps every Excel file you open. And there is no option to clear it or to disable it.
While you can individually select entries and trigger “Remove from Recent” from the context menu, there is no “Clear the whole list” action.
Irritatingly, there is a “Delete” option in the same context menu, that, indeed would delete the file and put it into the macOS trash bin.

This lack of functionality has been documented, discussed, and lamented for years now (e.g. here and here) and Microsoft said: nope.
Time for time travel, duh!
The last time I seriously did anything in VBA was decades ago, but hey, how much could have changed?
Not much, it turns out.
The following is a VBA macro, that clears the recently used file list and presents a dialog box afterward.
Here is the VBA code:
' This macro removes all entries from the recently used files list.
' It does not delete the files themselves though.
Sub deleteRecentlyUsedFilesList()
Dim listEntry
On Error Resume Next
For Each listEntry In Application.RecentFiles
listEntry.Delete
Next listEntry
MsgBox ("All done - list of recently used files cleared!")
End Sub
There is no error handling, so safety net, no nothing; so, if you want to use this, it is at your own risk.