The library RDCOMClient will be useful for you, here's what I could do on my side:
library(RDCOMClient)
ol <- COMCreate("outlook.Application")
objFolder <- ol$ActiveExplorer()$CurrentFolder()
objFolder$Items()$Count()
# [1] 489
The way it works is not straightforward and the doc of the package is not super easy, but here's how I find my way around it :
Use the VBA reference : https://learn.microsoft.com/en-us/office/vba/api/outlook.itemproperties
It gives you the object structure, it's sometimes easier to google than to navigate it directly.
Find out how people do it in regular VBA, and translate it in RDCOMClient syntax.
For example for this case I found on this link the following vba lines of code :
Set objFolder = Application.ActiveExplorer.CurrentFolder
EmailCount = objFolder.Items.Count
And translated them as shown above.
With a bit of trial and error, looking for existing code and tweaking with the vba reference you will hopefully find your way!