What is meant by "matter" (amr) in His, the Almighty’s, saying: (of every matter) and His saying: (therein is made distinct every wise matter)? And was Laylat al-Qadr named thus because the estimation of the religion and the Prophet's plan began in it, or for other meanings?

The meaning of "amr" (matter/affair) in the verse: (Therein is decreed every wise امر [matter/affair]) is everything that is ordained and predestined for the year, including lifespans, provisions, happiness, and misery. This is what Imam al-Tabari and other exegetes have chosen. As for the statement quoted in the question, it was not transmitted from the Salaf and there is no evidence for it.