When I used Windows, I had an easy way to copy a file’s path (generally on our server) directly from the Windows Explorer. Is there are an app that will allow me to do this on the Mac?

Yes, there is a fantastic app called Finder and it ships as part of the macOS! That’s right, it’s built-in, it’s just not noticed by most people.
Copy Path
You can copy a file or folder’s path by Right-Clicking the file or folder while holding the Option key down (as seen above) and choosing Copy “filenameXYZ” as Pathname from the contextual menu.

An even quicker way is by hitting Command + Option + C with the file/folder selected.

Doing either copies the path of the selected file or folder to the macOS clipboard—from there you can paste into any app.