I ran your city for a bit and messed around with a few things. I think your city might just have more efficient options compared to the public transport. Ofc I have no sense of how your city evolved over time and can't really compare to how it was when you had a lot higher public transport use.
Murdering your underground highway system gave a significant increase in public transport use (and ofc messed with traffic flow), which tells me that at least in some cases, it's just way more efficient than your public transport. The AI prioritises public transport, but only to a degree, so if alternate routes become much faster, then they will drive instead.
If I was moving forward with your city, I'd probably spend some time trying to improve the public transport setup, so it becomes a better option again. Alternately would be the option to work towards removing the underground highways and adjusting public transport and internal cargo rail to handle most of that traffic instead.