I'm not trying to force the Sabbath inside a day/commandment but rather look at what's does the Sabbath mean beyond the day/commandment. (I could have used "God's rest" instead) People seem very fixated on the day, I happen to think it is more than a day. A very basic purpose is simply "to obtain rest" but that's quite a loaded statement.
looking at the Sabbath in a creation vacuum Sabbath is the state of completion of God's work. We know God does not need to rest so we know this rest is not out of fatigue but because the works are complete. The creation account is a type of salvation metaphor, we know this because 2 Cor 4:6-7 tells us what the light of creation is about using the parallel that Christ "made light shine in our hearts" with a direct reference back to the creation account. light is contrasted with darkness and before light, the earth was unformed and existed in darkness so the salvation metaphors unfold naturally. before salvation we are in darkness then a process starts when light is spoken into use that forms us, fills us, and ends in rest.
the whole creation account is in a chiastic structure and the parallel chiasmus helps us understand the point being made. Day 1 is linked to day 4, day 2 is linked with day 5 and day 3 is linked to day 6 (for example day 2 the waters are separated forming the oceans/skies, day 5 fish/birds are filled in the oceans/skies). if you read the accounts you see the pattern of the first 3 days God is organizing/separating, and the last 3 days God is filling up and each unfolds in the same order. This covers days 1-6 but the rest of the account is still in a chiastic structure the first is in the first verse "in the beginning God created the heavens and the earth" which is paralleled with 2:1 "thus the heavens and the earth were created" and acts like bookends to the account.
There is only one parallel left and this is day 7 what does it link to? the only part left.
1:2 "Now the earth was formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters."
is paralleled with
2:2-3 "By the seventh day God had finished the work he had been doing; so on the seventh day he rested from all his work. Then God blessed the seventh day and made it holy, because on it he rested from all the work of creating that he had done.
I call it Day 0 and Day 7
so what does this tell us about the purpose of the Sabbath? it tells us it is the answer to Genesis 1:2. the answer that which is formless, empty and dark. So the Sabbath is the opposite and using the creation account we can see what the sabbath is and what it is not. the Sabbath is not formless it is formed, not empty it is full, not of darkness it is of light. And these are the exact focuses of the creation account, speaking light, forming, and filling until complete which ushers in the Sabbath. So the Sabbath is the state of fruition and culminating point of creation. Because God completed his work it is finished so it is holy and the work is rested and this is the Sabbath of creation.
The 4th commandment tells us to "remember the Sabbath day" (Ex 20:8) which connects it back to the beginning. It tells instructions on how to keep the Sabbath and gives us the reason and motivation in the law to keep it saying "For in six days the Lord made the heavens and the earth, the sea, and all that is in them, but he rested on the seventh day." (Ex 20:11) So the Sabbath day of law mirrors the rest God took on the 7th day. That rest, however, is not the rest of human fatigue it is the rest of a finished work that only God can do. The Sabbath day in the law tells us to remember a day but we can never achieve that kind of completion.
Hebrews 4:10 tells us "for anyone who enters God’s rest also rests from their works, just as God did from his." We first enter God's rest and the act of this invokes the rest from works too, "just as God did from his". We cannot rest as God did because that rest is contingent upon a finished work that only God can do. If creation is a salvation metaphor as 2 Cor 4:6-7 alludes to then that finished work is us. God doing a work in us starting by speaking light until complete and this is when we experience rest "just as God did form his"
This is embedded in the law itself as the law says "On it you shall not do any work, neither you, nor your son or daughter, nor your male or female servant, nor your animals, nor any foreigner residing in your towns." (Ex 20:10) this law is spoken to the heads of the households, those who have authority over the people in their household. it starts saying "you shall not do any work" then continues "neither you, nor your son or daughter, nor your male or female servant, nor your animals, nor any foreigner residing in your towns." so the context is clear that the "you" is the one with authority over the households. in ancient cultures explicit permission from the master is needed to do things in the household. this includes wives, children, servants/slaves, animals and even the people passing through the towns. This is especially clear with servants and animals, even more so with animals. A working animal cannot rest unless they are given that rest. if they lay down on the field in the middle of work they will be beaten. it is only when the master gives them rest that they may take rest and outside of that they have no authority to rest, even if they work to death they have no still have no authority to rest.
Our master is Christ and just as an Ox can only take rest if it is given by the master only Christ can give us rest and only he has authority over the rest. He says he is "Lord of the Sabbath" (Mat 12:8) which means the Sabbath is for him and he has authority over the Sabbath. He also offers us his rest (Mat 11:28-30). So Christ is the master of the Sabbath, he has authority over it and he offers us rest.
So with all that what is the purpose of the Sabbath? it is spiritual completeness that we receive through Christ, which is a parallel of the completeness of creation and Christ has the authority to give it. It is not just salvation but the completed works of the new creation in us (2 Cor 5:17) and because of this, just like the day, we are called blessed and holy.