Visual Studio Code is just a (fancy) text editor. If you are asking "Can I write an app using Visual Studio Code which I can use to check on file properties" - Yes, you can, although I'd suggest upgrading to full Visual Studio Essenstials.
You can know the date and time of when a file was modified by just looking at Windows "Last modified" column in file explorer. Should tell you the last time a file was saved.
I’m thinking they need more than that especially if this is in a development environment that involves a group of people modifying the same set of files