Psa 119:172 "..all thy commandments are righteous" that means obeying God's commands is doing/submitting to God's righteousness (Rom 10:3) and one cannot be of God until he does God's righteousness (commandments) 1 Jn 3:10.
He does not use "righteousness" to refer to God's commands.
If you insert that meaning of "righteousness" into Romans, you will misunderstand Paul's meaning.
Those Jews in Rom 10:3 were for they were doing their OWN righteousness and had not submitted/obeyed GOD'S righteousness.
Rom 4:13 "For the promise, that he should be the heir of the world, was not to Abraham, or to his seed, through the law, but through the righteousness of faith."
The promises given to Abraham were given not given through
the OT law of Moses and the flawless law-keeping that OT law required but was given to Abraham for he had an obedient,
righteous doing faith, that is, the promises were given through the right doing of Abrahams' faith (righteousness of faith)
Rom 4:13 "For the promise, that he should be the heir of the world, was not to Abraham, or to his seed, through the law, but through the righteousness of faith."
The promises given to Abraham were given not given through
the OT law of Moses and the flawless law-keeping that OT law required but was given to Abraham for he had an obedient,
righteous doing faith, that is, the promises were given through the right doing of Abrahams' faith (righteousness of faith)
There was only the law of circumcision.
Paul excludes "doing" (works) from the cause of Abraham's righteousness (Ro 4:2-3, 5-6, 9-11).