In Android Google Sheets, "enter key" (->|) won't move to cell below. How to fix?
It depends on the keyboard you are using. I tested it first with Gboard and secondly with Hacker's Keyboard and Microsoft SwiftKey Keyboard. With Gboard pressing Enter, insert a new line on the same cell. With Hacker's keyboard and Swiftkey, it takes you to the cell below. So, a possible solution is to use another keyboard (if GBoard is your default keyboard) while using Google Sheets.

Why is there not an option to specify &quot;enter&quot; key behavior, as in Excel?

That's a question Google developers (Gboard) will answer better than us as to why their keyboard behavior is different from the other (I have not found a webpage yet a reason for this behavior).

(Or is there one and that's what I can't find?)

There isn't one (for now).
Disclaimer: I am just a user of the mentioned keyboard apps.