What Happens if Earth's Axis is Not Tilted?

Hello! I have an interesting question that I'm hoping someone could answer. I understand that if Earth's axis was not tilted, it would mean that we would have no seasons. But what would happen to our Zodiac Constellations if Earth's axis was not tilted? Would our Zodiac Constellations still be the same, or would we have different Zodiac Constellations? In other words, if Earth's axis was not tilted, and Earth orbited exactly upright with respect to our orbit around the Sun, would the Sun pass through the same Zodiac Constellations that it passes through today, or would it pass through different constellations in the sky? I've had some tell me that if Earth's axis was not tilted today, the Sun would pass through the constellations that are currently along the celestial equator (i.e., Orion, Monoceros, Canis Minor, Hydra, Sextans, etc.) But I've also had some tell me that the Sun would still pass through the same constellations that are currently along the ecliptic plane (i.e., Taurus, Gemini, Cancer, Leo, etc.) I tend to agree with the latter answer because, if I'm not mistaken, the ecliptic plane never changes its position. Therefore, wouldn't it make more sense that if Earth's axis was not tilted, the celestial equator would align with the ecliptic plane rather than the other way around?