Back when I played the original Skyrim (and I played through it thoroughly, but never completed it), I spent quite a lot of hours exploring and doing quests. I also played the game with mods, but still experienced the Vanilla game as it should be played. One thing I never had was any of the DLC content and while I know they add new content to be picked up and found even in your main world space of Skyrim, there's other stuff that is questionable to me if it was added by DLC or just changes for Special Edition. Maybe it's my memory.

In the wilderness, I'm hearing more insects & birds and it's wonderful. The thunderstorms sound louder. You can hear pub noise outside and inside of taverns. Maybe it's all louder than it was before? Was this in the vanilla game 5 years ago, added by DLC, or new?

West of Whiterun at the West Watch Tower where you fight your first dragon, there's a fort just up ahead with bandits. Outside the entrance there's a guard post with steps that I don't remember seeing. Again, DLC or Special Edition? or has it always been there?

If you have anymore additions or changes that aren't mentioned, please mention them here!

I have completed the original multiple times, and I have been playing the SE version for quite a while. Besides the DLC, no specific content was added. However, there are many new effects, such as new snow and water shaders, god rays, and background fade (this is when the background fades when you are up close to an object. For example a conversation.) All the arts in the original were upgraded, and also came with a slight graphics upgrade. And yes you were right, new sound effects were added and the old ones were upgraded. Hopes this helps!

Cheers.

This video mentions a few hidden additions: https://www.youtube.com/watch?v=T6EjcESYIXk