You are correct in saying that the sabbath rest was made for man. I never heard anyone complain that they get to take a break from working. But there are two kinds of work, and two kinds of rest- physical and spiritual.
Jesus spoke in parables so that we can compare physical meanings to spiritual meanings, for a better understanding of spiritual matters. For example, He told Peter (the fisherman) to follow Him, and He would make him a fisher of men. Now if you take this literally (physically instead of spiritually) that would mean that Jesus would instruct Peter to cast a fishing pole toward humans, snag them with a hook, and pull them in. It is clear here that Jesus was speaking in the spiritual sense, and not in the physical sense.
The things that were done physically in the Old Testament are done spiritually in the New Testament. For example, David fought many physical battles for the Lord. Yet in Ephesians 6 the bible says our battles are no longer against flesh and blood, but are spiritual battles. Our armor is also a spiritual armor. (I could give many more examples, but I'm trying to make this as short as I can, if you want them just ask me).
The Old Testament Sabbath day is no exception. It was done physically in the Old Testament. You were forbidden to physically work on a physical day. But now there is a new sabbath rest for God’s people. When Jesus said, “Come to Me all you who are heavy laden and I will give you rest.” He didn't mean that if you go to Him He will take a heavy backpack off your back, or that He would have you quit physically working that day. He meant it in a spiritual sense. That He would take away your burden of sin (if you obey Him).
The physical sabbath day was only a shadow of the real thing- we will rest in heaven with God for all eternity. And we rest even now by casting all our anxieties and sins on Him. You know how Moses lead the people in the desert for forty years, and the disobedient died in the desert, so they did not enter Canaan? Physical Canaan represents spiritual heaven. If you read Hebrews 3:16 thru Hebrews 4:11. You will see that the disobedient did not enter God’s rest.
If you see how things were done physically in the Old Testament, but are now done spiritually in the New Testament, you'll see that they were just a shadow of the real thing. The real thing is the spiritual thing (Colossians 2:17). We are no longer under the physical sabbath, the physical lamb sacrifice, the physical high priest sacrificing animal blood for our sins.
These physical rituals did not save us (Hebrews 10:4), yet you are still trying to keep them alive even though we now have perfection- the real thing. What saved God’s people was obeying God until Christ’s sacrifice to pay for their sins. Then His blood flowed back to those in the past who obeyed God under the physical covenant, and to those in the present and in the future who were under the spiritual covenant. Jesus was sacrificed once for all who would obey Him. (Romans 6:10).
Songs
I don't know if you know these hymn lyrics, but if you do, can't you see how the physical only represented the spiritual? Much like a globe is not the real earth, it only represents the real earth…
To Canaan’s land I'm on my way (are we physically going to Canaan like they did in the Old Testament?) where the soul never dies (if we were physically going to physical Canaan, would we never die there?).
Oh land of rest for Thee I sigh, when will the moment come? When I shall lay my armor by and dwell in peace at Home (heaven) (this is the new sabbath rest). We’ll work till Jesus comes, we’ll work till Jesus comes, we’ll work till Jesus comes, then we’ll be gathered Home (to rest forever).