This resource on 'Ode to a Nightingale' by Keats says that the word "still" in stanza 6 ("Still wouldst thou sing") might have more than one meaning. However, I can't see it meaning anything beyond 'You would continue to sing'. Could there really by another viable interpretation?
While it's true that "still" is polysemous, I have a hard time justifying a reading of "dead" or "motionless" in this context. I could just as easily justify that the bird is making bootleg whiskey. "Still" is clearly describing the manner of the bird's singing, and the bird is not dead. Indeed, the next line is "Thou wast not born for death, immortal Bird!"
Rather than invoking multiple interpretations, I'd suggest looking at the other definitions as coloring the word here. The other possibilities exist in your mind as you read the poem, especially when you read it out loud. (Poems should almost always be thought of as spoken, rather than silent. They pack a lot of meaning into a few words, and the sounds and rhythm are part of that.) The line begins "Still" and you have a moment where all of the possible meanings of the word co-exist in your mind, and even after the rest of the line makes the surface meaning clear.
The concept of death pervades the stanza, and you will feel something different about that word, even in the same definition. A poem is like a painting: it means more than the sum of the brushstrokes, even if there's only one viable interpretation of the subject. The Mona Lisa is always a smiling person; the question is how it makes you feel, and how each brushstroke helps it achieve that feeling.
So I wouldn't look at this as an actor who might choose to pronounce the word as if it meant "dead". That is a valid way to approach a text, but in this case I think it would be a disservice to the poem; it would confuse the surface meaning. But you can enjoy the fact that those other meanings lurk there, and ask whether they do or do not affect how you feel about the poem as a whole.
The point I'm trying to make is that I think the study guide may be pointing you in the wrong direction with the way they've phrased the question. The word does have more than one meaning, and that does matter. But it's not a matter of treating it as a riddle to be decrypted, and where you've somehow missed the joke if you didn't get the hidden meaning. (This is a long-standing grudge with me: I didn't understand this until well after high school. I think it's common with the way nerds approach poetry. I don't know if it was the teacher who failed at that, or me, or if it's simply an unavoidable stage.)
I'd ask you instead to ask about the other ways he could have written that line. What if he'd said "Thou wouldst sing still"; what is gained or lost by the shift in focus on that word? What if he'd said "Yet wouldst thou sing" (and noting that "yet" also has multiple meanings)? I'm not looking for a judgment of better or worse; I don't even really know if Keats gave any consideration to writing it that way. (Though it can be fascinating to see rough drafts.)
It's a question of, "This poem is famous, and many people are moved by it. How does it achieve that, and does this particular element contribute to it?" Your answer can be "no", in fact, but the consideration is what helps you appreciate why you might want to read poetry. That's the lesson they're supposed to be teaching.
Still here is also an allusion to death, to being still, to no longer being alive, or moving.
"Allusion" means to refer to something without mentioning it directly, which is what poets do.
So, still here has a double meaning (a noted Keats device) of being a synonym for nonetheless, and also a reference to death.
So it seems to me, anyway.