Well Hebrews 10 is mainly about animal sacrifices, so 'no more sacrifice for sins' is no more animal sacrifice, since that is what the Hebrews were returning to. They were going back to sacrifice of sheep, bulls and goats, even though they were under the New Covenant.
Yeah but it’s really a constant contrast between the things of the ot ( like animal sacrifices and sinful preists the shadows ) and the true things of Christ Jesus flesh and blood and his preisthood in the true tabernacle ect
The whole book is an argument to Hebrews that there’s a new covenant a better one before them . So you see the constant contrast even from the beginning Jesus is compared to the angels who ordained the old and exalted far above them . Each section of the covenant is compared the sacrifices , the tabernacle the preisthood the covenant promises , the promised land of the covenants
notice there’s a constant contrast like Moses words and animals blood v the blood of Christ and his better words of mediation. Like sinful imperfect preists v a perfect priest who faced every temptation of men and never sinned proving his perfection and becoming the intercessor of those who believe.
The whole book does just what you say correctly there aboit animal sacrifices of the old the sacrifice of Jesus Christs body and blood of the new
Its a whole argument regarding the two covenants
“Then verily
the first covenant had also ordinances of divine service, and a worldly sanctuary.
……But
Christ being come an high priest of good things to come, by a greater and more perfect tabernacle, not made with hands, that is to say, not of this building;
neither by the blood of goats and calves, but by his own blood he entered in once into the holy place, having obtained eternal redemption for us.
For
if the blood of bulls and of goats, and the ashes of an heifer sprinkling the unclean, sanctifieth to the purifying of the flesh:
how much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God?
And
for this cause he is the mediator of the new testament, that by means of death, for the redemption of the transgressions that were under the first testament, they which are called might receive the promise of eternal inheritance.”
Hebrews 9:1, 11-15 KJV
Really it’s just a single letter they added the chapters and verse numbers for study but if we read through it it’s just one long argument to Hebrews that there is a new covenant and thier old one was inferior in every way
