Hebrews 4 is not referring to the Saturday Sabbath, but it is referring to laboring to enter into the rest of Christ Jesus. Jesus is our Sabbath rest.
Verse 11 refers to how we need to labor to enter into this rest otherwise (lest) that person will fall away by the same example of unbelief.
Let us therefore come boldly unto the throne of grace, that we may obtain mercy, and find grace to help in time of need.” (Hebrews 4:16).
Jesus says, “Come unto me, all ye that labour and are heavy laden, and I will give you rest.” (Matthew 11:28)
Jesus is our Sabbath rest. It is not the Sabbath day anymore.
Hebrews 3-4 (among many others; John 14:15; Exodus 20:6; Isaiah 56:1,8; John 10:16; Isaiah 56:2-7, Acts 4:24, 14:15; Revelation 10:6, 14:6-7, &c).
Hebrews 3-4 is clear.
Hebrews 4:3, "my (God's) rest" and "the works were finished from the foundation of the world", which is a direct reference to Genesis 2:1-3. It even uses the word "finished". God rested the 7th day in Genesis 2:1-3. It is His rest, the 7th day, the sabbath (rest) of the LORD thy God, Exodus 20:8-11.
Hebrews 4:4, "he spake in a certain place of the seventh day on this wise, And God did rest the seventh day from all his works", which "certain place" is Genesis 2:1-3; re-cited in Exodus 20:8-11. The 7th day the sabbath (rest) of the LORD thy God.
Hebrews 4:5, "my (God's) rest)", citing Psalms 95, which is citing Genesis 2:1-3; Exodus 20:8-11, etc. Again, this is the 7th day the sabbath (rest) of God at Creation in Genesis 2:1-3.
Hebrews 4:6, "remaineth", from when? "from the foundation of the world" as per Hebrews 4:3 and thus it is not new, but has been around from the beginning.
Hebrews 4:9, "rest", sabbatismos, literally and truly sabbath keeping in scripture and in all known extant Greek sources, dictionaries, and so on and again "remaineth".
Hebrews 4:10, "his (God's) rest", which is the 7th day the sabbath (rest) of the LORD thy God from Genesis 2:1-3., "as God did from his (works)", which "works were finished from the foundation of the world" as per Hebrews 4:3.
Hebrews 4:11, "that rest" (ie God's rest), the 7th day the sabbath (rest) of the LORD thy God.
P.S., every single reference that uses the word "sabbatismos" in written documents, always refers to the seventh day.