You're right — and it isn't only on ropes. Pets are drawn behind your character everywhere in the game right now; a rope or ladder is just the one place where the pet sits right on top of you, so it's the only place you can see it.

Both of the v83 client sources draw the character first and then the pets on top of them, so a pet should always be in front of its owner. Ours was ordered just behind the character, which is why your pet is half-hidden by your sleeve in that shot.

Fixed by moving pets above the character in the draw order. While I was in there I also noticed the pet's name plate was being left behind at the bottom of the rope while the pet itself climbed with you, so that now follows properly too. The hanging pose your pet is using is already the correct one, so that part stays.

Fix shipped — this is now on develop and will be in the next build.

The diagnosis is in the comment above; this is just to confirm the change is written, type-checked, built and pushed rather than only planned. Please re-test when the next build goes up and reopen if it is still wrong.