Is what happens within oneself, such as imagining a specific person and subsequently laughing at these thoughts or words to oneself, considered to be a matter of legal embarrassment (haraj shar'i)?

If these imaginings are mere self-talk that do not settle in the heart, then there is no accountability for them, according to the Prophet's (peace be upon him) saying: "Indeed, Allah has pardoned my nation for whatever they whisper to themselves, as long as they do not act upon it or speak of it." However, if these imaginings lead to ill-conjecture about Muslims whose outward appearance is one of uprightness, then they are unlawful.

As for these imaginings, if they are deliberately summoned, settle in the heart, and one laughs at them by choice, then this is not permissible. Fleeting thoughts and self-talk are pardoned as long as they do not settle. What is possible is to avoid persistence in them, for persistence and holding them in the heart is unlawful. And thoughts related to sins must be repelled by turning away from them.