
The answer is deceptively simple, click on the Format Icon in the top-right corner of the document window. The Function Browser visibility state is bound (disastrously IMHO) to the state of the Format tools sidebar. There is no UI hinting or Numbers help topics, or Menu Item "Show Function Browser" / "Hide Function Browser" state toggle or any other hints that these two things are bound.
If the Format sidebar is not showing it's easy enough to look around and see the word "Format" and there's a bunch of help topics to find it. Not so for the Function Browser. I provided Apple with some Feedback. I hope they fix this to some extent at least with a Fx Menu item to show the Function Browser or some other kind of toggle on the Equation Editor floating window or the main document window or in the App menus. Preferably with or more than one solution to make it more discoverable. And putting something in the Help that comes up when you put Function Browser into the Help> Search field would be a good idea I think.
If the Function Browser goes missing when you click in a formula or a cell set to take a formula, its because either:
A) the user clicked on the Format Icon (top-right corner of document window) to hide the Format sidebar tools
B) clicked on the Organise Icon to Sort, Filter,… a table, in which case there is just a blank grey space where the Function Browser should be appearing when working with an Equation. That's more of a hint at least.
Doing either of these things will determine that when a formula text is selected, the Formula Browser does not appear on the right hand side of the document window.

when in hidden state:

when in visible state:
