The context all relates to the spiritual rest of faith, entered into "today." You have inserted the weekly Sabbath into verse 9. But even the authors of the SDA Bible commentary didn't agree with that because the context doesn't match up.
You appear to be using the term in a technical sense that is limited to only the weekly Sabbath. But this is not accurate.
This is the only instance in Scripture of the word, but we have usage that do not relate to the weekly Sabbath, such as in Origin.
Origen On Prayer, 17
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When a man has had vision of these things and has given thought to a week of ages with intent to contemplate a kind of holy sabbath—keeping and a month of ages to see God’s holy new moon, and a year of ages to survey the feasts of the year when every male must appear before the Lord God, and the corresponding years of so many ages to discern the seventh holy year, and seven weekly years of ages to sing a hymn to the Enactor of Laws so great, how can he after such consideration cavil over what is the merest fraction of an hour in the day of such an age, instead of doing everything to become, through his preparation here, worthy of obtaining the needful bread and to receive it while it is today and daily, what daily means being already clear from the foregoing explanations.
Here Origin relates the word to a week of ages sabbath keeping, which is certainly beyond a description of a literal 7th day Sabbath observance.
Moreover, as the SDA Bible Commentary authors, as well as others, have noted, the verbal form is used interchangeably with the other term for rest in the LXX.
And we have a commentary on this passage from a native Greek speaker closer to the time who recognizes the word means a sabbath rest, but does not point to the weekly Sabbath.
Note, I don't quote him in this case so you may consider him authoritative in his theology, but in regards to the Greek usage, as that is part of your argument.
Some highlights from Chrysostom's comments on Hebrews 3-4:
When David then, he says, speaking at a later period, and after these events, after that generation of men, said, Today, if you will hear His voice, harden not your hearts, that you may not suffer the same things which your forefathers did, and be deprived of the Rest; he evidently said this as of some [future] rest. For if they had received their Rest he says why does He again say to them, Today if you will hear His voice harden not your hearts, as your fathers did? What other rest then is there, except the kingdom of Heaven, of which the Sabbath was an image and type?
What then does he say? Hebrews 4:9 There remains therefore a rest for the people of God. And see how he has summed up the whole argument. He swore, says he, to those former ones, that they should not enter into the rest, and they did not enter in. Then long after their time discoursing to the Jews, he says, Harden not your hearts, as your fathers, showing that there is another rest. For of Palestine we have not to speak: for they were already in possession of it. Nor can he be speaking of the seventh; for surely he was not discoursing about that which had taken place long before. It follows therefore that he hints at some other, that which is rest indeed.
And well did he conclude the argument. For he said not rest but Sabbath-keeping; calling the kingdom Sabbath-keeping, by the appropriate name, and that which they rejoiced in and were attracted by.
For that is indeed rest, where pain, sorrow and sighing are fled away Isaiah 35:10: where there are neither cares, nor labors, nor struggle, nor fear stunning and shaking the soul; but only that fear of God which is full of delight. There is not, In the sweat of your face you shall eat your bread, nor thorns and thistles Genesis 3:19; no longer, In sorrow you shall bring forth children, and to your husband shall be your desire and he shall rule over you. Genesis 3:16 All is peace, joy, gladness, pleasure, goodness, gentleness. There is no jealousy, nor envy, no sickness, no death whether of the body, or that of the soul. There is no darkness nor night; all [is] day, all light, all things are bright. It is not possible to be weary, it is not possible to be satiated: we shall always persevere in the desire of good things. Homily on Hebrews, John Chrysostom, Arch-bishop of Constantinople.
He applies it to rest in the kingdom of God.
You disagreed with the SDA Bible commentary I quoted from earlier, but didn't address their linguistic and contextual arguments.
Accordingly, the fundamental idea expressed by sabbizo in the LXX is that of rest or ceasing from labor or other activity. Hence usage of the related Greek and Hebrew words implies that the noun sabbatismos may denote either the literal Sabbath "rest" or simply "rest" or "cessation" in a more general sense. Thus, a linguistic study of the word sabbatismos in Heb. 4:9 leaves it uncertain whether the weekly Sabbath "rest" is here referred to, or simply "rest or "cessation" in a general sense.
The writer of Hebrews appears to use katapausis and sabbatismos more or less synonymously. Because Joshua could not lead Israel into spiritual "rest" (katapausis, v. 8), a sabbatismos (v. 9) remains for Christians. Consistency seems to require that what remains be the same as what was there to begin with. Because Joshua did not lead literal Israel into spiritual "rest" would be no reason for the Christian to observe the Sabbath.
From vs. 1, 6 it is clear that what remains for the people of God in NT times is a katapausis; in v. 9 it is said that a sabbatismos remains.
The fact that in the LXX, the Bible of the NT church, Katapauo (Gen. 2:2, 3; Ex. 20:11) and sabbatizo (Ex. 16:30; Lev. 23:32) are used interchangeably to denote the seventh-day Sabbath, would tend to preclude the suggestion that the writer of Hebrews intended to make a distinction between the noun forms of these words in Hebrews 3; 4.
Furthermore, it may be observed that the section of the book of Hebrews consisting of chs. 3 and 4 opened with an invitation to "consider the Apostle and High Priest of our profession, Christ Jesus" (ch. 3:1), and closes with an earnest plea to "come boldly" before Him in order to "obtain mercy, and find grace to help in time of need" (ch. 4:16). What relationship a protracted argument designed to prove Sabbath observance remains an obligation to the Christian church might have to the declared theme of chs. 3 and 4--the ministry of Christ as our great High Priest in the heavenly sanctuary--is obscure indeed.
Then the SDA Bible Commentary quotes Ellen White on the subject:
"The rest here spoken of is the rest of grace" (EGW Supplementary Material on Heb. 4:9) From Letters and Manuscripts — Volume 16 (1901)
And they provide this quote, but I have put in additional context to see even more clearly:
And thus the mountain from which the words of benediction were spoken came to be known as the mount of blessing. But it was not upon Gerizim that the words were spoken which have come as a benediction to a sinning and sorrowing world. Israel fell short of the high ideal which had been set before her. Another than Joshua must guide His people to the true rest of faith. No longer is Gerizim known as the mount of the Beatitudes, but that unnamed mountain beside the Lake of Gennesaret, where Jesus spoke the words of blessing to His disciples and the multitude.
Ellen White--Thoughts from the Mount of Blessing Chapter 1
