No, doing something is never necessary (that would make salvation earned by a good work).
The Sabbath in the OT was a picture of our rest in Christ all the time, we need daily sabbath in Him. Yet literally ceasing from labor to be refreshed and restored was part of God’s design in a perfect, unfallen Eden. If we are obedient to the Lord, we must accept His gift of Sabbath. The particular day on which we do so is not mandated. Sabbath is not a legalistic work, just like generous giving, it is a gift from the Lord to share in and partake of.
“One person esteems one day above another; another esteems every day alike. Let each be fully convinced in his own mind. He who observes the day, observes it to the Lord; and he who does not observe the day, to the Lord he does not observe it. He who eats, eats to the Lord, for he gives God thanks; and he who does not eat, to the Lord he does not eat, and gives God thanks. For none of us lives to himself, and no one dies to himself. For if we live, we live to the Lord; and if we die, we die to the Lord. Therefore, whether we live or die, we are the Lord’s.” Romans 14:5-8
“Thus the heavens and the earth, and all the host of them, were finished. And on the seventh day God ended His work which He had done, and He rested on the seventh day from all His work which He had done. Then God blessed the seventh day and sanctified it, because in it He rested from all His work which God had created and made.” Genesis 2:1-3
“There remains therefore a rest for the people of God. For he who has entered His rest has himself also ceased from his works as God did from His.” Hebrews 4:9-10
“For by grace you have been saved through faith, and that not of yourselves; it is the gift of God, not of works, lest anyone should boast. For we are His workmanship, created in Christ Jesus for good works, which God prepared beforehand that we should walk in them. Ephesians 2:8-10