What is the difference between he left without saying goodbye and he left without so much as saying goodbye ?Feel free to just provide example sentences.

‘Without so much as’ is emphasizing (strongly suggests) that they did not even do that, when you were expecting them to do that. (Like someone broke the rules.)
It does have a negative feeling.
For example... there is a restaurant that asks you take off you shoes before coming in. But someone comes in with out taking off their shoes. So you might say to someone else ( They came in with without so much as taking off their shoes.) You say this because you thought they would and you are annoyed they didn’t follow the rules.