Is any harsh talk with parents considered disobedience, even if it's in a tone of voice that indicates annoyance without shouting? And must one seek their forgiveness immediately if that would make them lenient regarding the questioner's rights?

If the parents are hurt by the manner of speech, a hurt that is not trivial, then it is not permissible to address them in that way, and one must seek their forgiveness. Otherwise, it is not considered disobedience. The forbidden disobedience (aqūq) is every action that hurts the parent in a way that is not trivial, unless the action is obligatory. The criterion for disobedience is harming them in any way, whether little or much, or disobeying them in what they command or forbid, provided there is no sin involved. One must strive to be dutiful to parents and address them with gentle, non-harsh speech, in obedience to Allah's command: "And speak to them a noble word And lower to them the wing of humility out of mercy." One should not say or do anything that would harm them, but rather be humble towards them and supplicate for them.