Based on what I can access right now, the precession of Earth's axes are in a cone shape, so there isn't much wobble. But with all of those Near-Earth Objects, and nearby planets, there is probably some wobble (I'm no professional).
There's also this thing called the Milankovitch Cycle, which shows how the combined effects of precession, external forces, and etc. affect climate. It also affects the eccentricity, or the circularity, of Earth's orbit in a cycle of 430,000 years. This affects seasonal length and season intensity. It also changes orbit orientation, so the perihelion and aphelion move to different locations. If you want to learn more, read https://en.wikipedia.org/wiki/Milankovitch_cycles.
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