I understand that the price of a tunnel is somewhat comparable to the bridge.
What gives you your understanding? Mine is from multiple sources at the top of Google for the query "price of tunnel versus price of bridge"
Engineering costs its a matter of volume, what kind of ground you need to dig, expertise and experience. If you can get something like the Boring company up, costs would drop down.
And engineering costs don’t account for externalities of having a bridge full of noisy cars hanging there, polluting in every modality: view, noise, smell, splitting the neighborhood, reducing walkability, destroying the property value.