Sorry, I’m not quite sure I understand your question?
In early Z-machine versions (3 and earlier) the status line is handled completely by the interpreter: it displays the name of the object referenced by a certain global variable on the left, and either score/moves or hours:minutes from two globals on the right (choice of format based on a header flag). The exact formatting is up to the interpreter, so it can vary widely across systems.
In version 4 and onward, the status line is handled by the game: the interpreter just provides a system to draw whatever the game wants. Which might be a classic v3-esque status line, or just the location name centered (as in Trinity), or anything else.
So my guess is, the only games whose status lines vary across interpreters are the v3 and previous ones. And for those, it’s up to the interpreter writers rather than the game writers to decide how modern terps should display them.
Apologies if this is all old information to you: just let me know if I misunderstood your question!