"do [something] now". How to interpret this?

Yes, it sounds like it's intentional, to indicate that they expect the thing to be done straight away without any further discussion or questions.

To replace a negative thought with a positive one, maybe she is just pressed with time and focuses on just delivering the message rather than being polite.

Stop what you are doing, and do this now.

is shorter than

Could you stop what you are doing, and do this instead, please.

Many of us get so lazy to write full sentences while communicating with others online, especially in a stressful environment at work. It affects the quality of our language and, as you say, it has an impact on our relationships. I guess politeness does take a bit of time...

Out of curiosity I searched Gngram, and it shows that do this now is much more frequent than do this instead.

The request is direct and thus may be perceived as rude. To think about the statement more clearly, it helps to consider a few factors.

Imperative mood

Do this now is an imperative clause (ThoughtCo), which conveys a command or request that you comply immediately. The use of imperative mood is more direct, which depending on context (see the third factor) may be perceived as less polite than making a request in other moods, e.g.:

Would you do this now? (indicative mood)

I think you should do this now. (indicative mood)

I wish this were done. (subjunctive mood)

Function words like please

The statement can also be made more or less polite by what you add to it. For instance, please (Merriam-Webster) is a function word that makes a request more polite. That is one tool that could slightly mollify the demand made:

Please do this now.

Would you please do this now?

I think you should do this now, please.

For an example of a much ruder addition, consider this:

Fucking do this now.

Context and Now

Now makes the demand more immediate, which may be rude in contexts where the addressee has other tasks and obligations. Rudeness with a word like now is going to be circumstantial and heavily dependent on context. For instance, in an instructional space like an ASVAB test, the administrator might say:

Now look at the section of your answer sheet labeled "PRACTICE”. Notice that answer space C has been marked for question S1. Now do practice questions S2 and S3 by yourself. Find the correct answer to the question, then mark the space on your answer sheet that has the same letter as the answer you picked. Do this now.

The clauses are imperative. The context is one where imperatives for the sake of test instructions are expected. The now clarifies that students should act at that moment, and is not a sign of rudeness.

So I wouldn't read now as something inherently rude, but would think about that carefully in the context it's delivered in.