Righteousness is, indeed, a word that combines all aspects of goodness, theoretical and practical, relating to the treatment of people, to worship of the Creator and to a lofty morality.
It is with all these that true believers should be preoccupied.
Consider also how when the surah begins to detail these aspects, it does not relate them all, in full, at the same time.
Rather, it moves towards them progressively, beginning with a statement that gives more than a general idea, but which remains short of giving them in full detail.
Thus, it serves as an index to the principles of faith and to the codes of Islam:
“But truly righteous is he who believes in God and the Last Day, and the angels and the Book and the Prophets; and gives his money, much as it is dear to him, to his kinsfolk,
to the orphans, to the needy, to the traveller in need, and the beggars and for the freeing of slaves; who attends to his prayers and pays zakat;
[and righteous are they] who remain true to their promises whenever they promise, and are patient in misfortune and adversity and in the time of peril. Such are those who have proved themselves to be true, and such are those who fear God.”
(2: 177.)