Is expressing annoyance bad karma?

No, good householder, not is not pleasing for others speech bad kamma, when right and acrually with wholesome mind. Given that right, and out of compassion, even harsh speech can be heaven leading conduct.

Not seldom the Buddha used harsh speech and not seldom declared his annoyance, yet good to keep in mind that 1. it was right, 2. out of compassion, 3. himself no faults, 4. unrelated, no trouble with possible bad reactions on it.

For example, my person often rebukes Nyom OyaMist here because of his poor and worldly biased ways to cite the Buddhas words from a Robin Hood-thief undertaking group. He and many, will think: "oh, what bad and unrighteous kamma, again, and again, by this monk." ... understandable?

At least he had learned that dukkatha, in the context of talking about virtue with unvirtuoes, about generosity, with a greedy... wisdom, with one without wisdom, isn't faulty but simply burdensome... yet still seeks to defend the "hot dogs for everyone Dhamma", as not willing to let go of pseudo-liberalism, authority-rejecting, and marx-ideas, wrong view of the basic one: equal we are... So here as sample to investigate and out of compassion Dispraise and "harsh speech" (gross to get one to mind)!

Usually those after "soft speech", are those who kill off and take ungiven simply hidden and silently and use "speak nice" to block off what goes against free consume and endanger beloved taken on stand, view.

It may "That lack of useful information", desired food, consume, yes. Like bitter medicine.

Summary: neither neutral nor wrong, but good and right, the highest, if spoken timely (when proper ocassion)

Maybe in addition good to know that one does not really have certain duty to help another out by using straight words, at least not in harsh way, if not in relationship, since in can take years, if even, till the message arrives.

May one try in saying for example, after good prove: "Jewish is actually the most fascist religion." on a consume page... dhammic correct will lead one apart from consuming "political correct" speakers. Which is actually not for ones lose, since right view is much more of worth that relationships and certain gains by it.

As for "annoyance at what is perceived as unfair treatment": maybe good to investigate the topic "Justice vs. skillfullness" and "Wisdom over Justice", to learn about right judgement, because it's mostly that speech on such isn't wholesome but often based on wrong view. Anger is always akusala, yet one should only kill it ;-).

When a wheel turns, it brings us passage with ease to new places. If there is sand in the axle, there is friction and resistance. Annoyance is felt as passage becomes difficult.

If two people are travelling by cart, one of them may notice difficulty and tell the other, "the wheel is not turning well." At that point the other may respond, "this is a good place to stop and check". Or they might respond, "this is a bad place to stop and check". This is a simple and good interaction.

However, when identity view enters, things get messy. With identity view we might be frustrated and annoyed at not getting what we want and then we might look about for things we can fix. Looking about, we might notice that the person sitting next to us is happily sleeping and that happiness might make us feel even more annoyed. We might even be quite indignant at that person next to us. Being indignant, we might kick them off the cart. That is a poor interaction that leads to much suffering and has nothing to do with the wheel not turning well.

The trouble with identity view is that it limits us in mind, speech and body. Identity view masks and excludes others. Identity view asserts, "I am annoyed." Identity view is the sand on the axle that impedes smooth travel.

Putting aside identity view allows us to interact smoothly and effectively with others. We can turn to them for help in working on a mutually experienced problem. We might stop the cart. We might shake our sleepy friend awake and say. "There is a problem here and night is coming. Let us fix it together. Please help me lift the cart so that we may check the wheel."

Now shaking a happily sleeping person might be very annoying to them and they might be angry and resentful. But that, too, is identity view, "My happy sleep has been taken away and I don't like that." Identity view has not helped here either. A better reaction to being shaken awake might simply be, "what is happening?".

What's common here is that identity view leads to bad kamma and poor interactions.

MN129:1.6: The Buddha said this:
MN129:2.1: “These are the three characteristics, signs, and manifestations of a fool.
MN129:2.2: What three?
MN129:2.3: A fool thinks poorly, speaks poorly, and acts poorly.

Expressing annoyance is quite often counter-productive. If there is annoyance, there is a problem that we may need help with. And if we need to express anything, perhaps what works best is to communicate what is actually needed (i.e., "wake up, please. We have a problem.") as opposed to what is felt (i.e., "why are you sleeping happily and ignoring our problem?").

Expressing annoyance is often imprudent and foolish.

MN8:12.25: ‘Others will be irritable, but here we will be without anger.’

MN8:12.8: ‘Others will speak harshly, but here we will not speak harshly.’

MN8:12.40: ‘Others will be imprudent, but here we will be prudent.’

If help is needed, it is better to communicate the actual need, not the annoyance. Expressing annoyance often just spreads it around. Expressing annoyance provides little actual information--it is unhelpful. And because expressing annoyance is unhelpful, people won't be inclined to help, unless they are extraordinarily patient. Lack of help would then be the expected outcome (kamma) of expressing annoyance.

Expressing annoyance is not neutral. We commonly express annoyance in order to goad others to action. But there are better ways to goad others to action. Expressing annoyance is unskillful. Annoyance conveys urgency but no other information. That lack of useful information is what leads to "bad kamma".

MN129:2.3: Idha, bhikkhave, bālo duccintitacintī ca hoti dubbhāsitabhāsī ca dukkaṭakammakārī ca.
MN129:2.3: A fool thinks poorly, speaks poorly, and acts poorly.

The key phrase here is dukkaṭakammakārī, which may be understood as action leading to suffering (i.e., foolish). Expressing annoyance falls under "speaks poorly". In that sense expressing annoyance is not prohibited by any specific rule, but presented as inadvisable in the context of poor speech (v.s. wrong speech).