Currently, the drawer at the bottom of the screen that displays details about the selected suggestion and buttons to interact with it is implemented as a ContextItem that is displayed by VE's context system when the cursor is inside a suggested link. This seemed like the easy way to do it because it's how other annotations are inspected and manipulated in VE, but it has some issues.
Context items are ephemeral, meaning they are rerendered from scratch every time a different annotation is selected or the annotation changes (because annotations aren't editable either, changing a suggestion from undecided to accepted requires blowing it away and reannotating the text with a slightly different suggestion annotation). This is wasteful, and would also make it quite difficult to implement things like transitions for navigating between suggestions.
The context can't be activated manually, it activates automatically based on whether the selection is inside a matching annotation. However, because link annotations are nailed, there are selection management issues that make it difficult for us to convince the context to open or stay open when we want it to (see T267705: Add a link in VE: issues with opening context when selection is at the edges of an annotation).
We should consider using our own context instead of VE's, and have that permanently live at the bottom of the screen. This could simplify a lot of these issues, and could also make it easier to implement the desired design on desktop (where the context defaults to appearing inline at the cursor, instead of at the bottom of the screen).