How did the question of slavery become linked to the new US Constitution?

During the Constitutional Convention, a great debate occurred between representatives from slave states and those from free states concerning the issues of taxation and representation. The framers of the Constitution were at odds as to how slavery would be permitted and addressed in the new United States. Slave states wanted slaves included in census counts in order to assign those states more representation in Congress. The irony is that although these states wanted slaves to count toward the delegation of congressional representatives and the allotment of federal funds, they did not want slaves to be beneficiaries of this situation. The Northern states were afraid that if slaves were included in population counts, then these otherwise less-populated states would have a disproportionate amount of representation in federal government.
A compromise was reached in which each slave would be counted as three-fifths of a person when concerning representation and taxation. This compromise was enshrined in Article I, Section II of the Constitution which states that

Representatives and direct Taxes shall be apportioned among the several States which may be included within this Union, according to their respective Numbers, which shall be determined by adding to the whole Number of free Persons, including those bound to Service for a Term of Years, and excluding Indians not taxed, three fifths of all other Persons

While it does not mention slavery by name, it is implicit that "all other Persons" refers to the enslaved population of the Southern states.
Further mention of slavery is made in Article I, Section IX, which permits a "Tax or duty may be imposed on such Importation" of African slaves. Article IV, Section II deals with runaway slaves, decreeing that they must be returned to their original state if found in another one.
All these clauses enshrined slavery into law and wove slavery into the fabric of the nation. It would not be until the ratification of the Thirteenth Amendment in 1865 that slavery was constitutionally outlawed in the United States.
https://ashbrook.org/publications/respub-v6n1-boyd/

https://www.archives.gov/founding-docs/constitution-transcript