Difference – ‘I Have an Emergency’ vs. ‘I’m Having an Emergency’

I you are talking about your continued employment at a company, or just the fact that you aren't retired, then both phrases mean the same.

If you are talking about a task you are engaged in at the moment, then "I am still working." is idiomatic.
But in that context, "I still work." isn't idiomatic.

Non-native speakers tend to forget that English when spoken has additional tools than those available in writing. The most important is volume.

I insist

and

I am insisting

where the bolded words are stressed have identical meanings. It is not the words but rather the volume that gives emphasis in speech.

A skilled writer will recognize that present and present continuous seldom represent different degrees of emphasis. In any case, “insist” is emphatic in its very meaning. You can supply emphasis through auxiliary verbs

I must insist

or

I do insist

And of course adverbs can provide emphasis

I absolutely insist

To go back to your original question. In the rare cases where there is a difference in emphasis between present and present continuous, the present is more emphatic because present continuous is focused on the immediate instant. If, after a fight with your significant other, you say

I am loving you

you will be sending a less reassuring message of affection than

I love you

In short, tense is not the most usual way to signal emphasis.