The plastic liner is genuinely breaking down. Those polymers weren't meant to handle constant temperature swings from hot water fills and cold storage, especially over a full year of daily use. The smell you're catching is volatile organic compounds (VOCs) being released as the material degrades. You're not paranoid - your nose is picking up a real chemical process.
Here's the thing though: most people focus on cleaning the bottle itself, but they miss that the liner is the source. Scrubbing and baking soda won't help because the degradation is happening inside the polymer structure, not on the surface. What actually works is getting the bottle to off-gas faster. Leave it uncapped in direct sunlight for a few hours a day for a week or two. Heat and UV light accelerate the release of those compounds, and then they just dissipate. Some folks also report success running it through the dishwasher on high heat repeatedly, though that can speed up further degradation.
The real pitfall is that once a plastic liner starts breaking down, you're fighting a losing battle. Even if you get the smell mostly gone, it'll come back. If you want this bottle long-term, you might consider replacing it with one that's fully stainless steel inside, or switching to glass. A decent stainless steel bottle without a lining usually costs about the same as what you spent on that one and actually lasts.