@D-A-Wakefield, this is really hard to understand, so I will make some assumptions, correct me if I am wrong.
You are using the (web)App on your computer. Let's not call that App because it makes people think you are using the Android/IOS app. Let's call it Webapp, or "in the browser", or "on my computer"
If you create a new route in the correct way, it should autosave without further action. There is no Save button anywhere.
From the homescreen press "New Route"

A popup pops up
asking for route name etc. After pressing OK you enter the planner and all changes you make are stored immediately without any need to "save" (that's oldskool
)
If you use the roundtrip generator, after pressing Next the same thing happens as before. A name is suggested, you can rename it if you want, and when you press "Use this route" (or similar), that route immediately is stored in your personal library (simply named "Routes").