What do you mean by the path button?
Your screenshot shows a selection made by the elliptical marquee tool. It's not a path....
Hi! Can you please explain your problem better?
By the way, have you tried by selecting The Paths panel (Window > Paths)?
Something that makes a lot of sense to me is to sort out, and save, a more useful workspace when you first start using a new install of Photoshop. You need to look at the default workspace with a tiny touch of cynicism — the Library panel is right there in your face, because Adobe are pushing Adobe Stock like crazy as an additional revenue stream. Start with the workspace most appropriate for you. Maybe the Photography workspace for instance. Have your major panels open on the right, and grow the auto expanding icons along side the major panels. One click opens the thumbnails, and another click collapses them.
I cobbled this workspace below by way of demonstration (I use three screens so don't normally work this way). In the case of your question, you'd have had the Make work path from selection icon right there ready to use.
Save your new workspace. You can now drag out a panel to make it more convenient, and Reset your work space to get back to default. The Essentials workspace is hard wired, and the go to method of making sure you seeing everything in as standard.
One more thing that I advise, (but you might like to do it differently) is to have these options unchecked. It is annoying in the extreme to have those collapsed panels fly in and out for no apparent reason.
I am now using Photoshop 2018 and I am creating a vector mask with the Ellipse Tool. I don't see the Path option from the Options bar and I do not see the Combine Shapes option either. Are these options removed from or hidden in Photoshop 2018?