What are the observations regarding this anecdote, and does it contain any forbidden شرعية (religiously illicit) elements?

Jokes and similar forms of idle talk (laghw) refer to all words and actions that are of no benefit. This is based on the Almighty's saying: "And those who turn away from idle talk" (Quran 23:3). Idle talk encompasses falsehood, sins, and words and actions that are of no benefit. The predecessors used to avoid such talk, even if it contained no sin, out of fear of falling into what is sinful, and out of a desire to occupy their time with what is beneficial, to accumulate good deeds, and to minimize what is useless.

Every responsible individual should guard their tongue from all speech except that in which there is a clear benefit. If speaking and refraining from speaking are equal in terms of benefit, then the Sunnah is to refrain from speaking, based on the Prophet's (peace be upon him) saying: "Whoever believes in Allah and the Last Day, let him speak good or remain silent."

The advice is to abandon the circulation of such jokes and to engage in what is beneficial.