No it doesn’t. The condition of slavery wasn’t addressed by interpreting “people” to exclude enslaved people, additional words were added to distinguish enslaved people from free people. But free Black people, for example, were always included in the count of “free persons.” Other laws may have imposed limits. In 1789 women couldn’t vote and in 2021 children still can’t. But they were all included in the definition of “people.” Those other laws changed but the meaning of “people” didn’t.
The first half of your argument is about how the constitution specifies citizens (a subset of people) with "we the people". The second half is about how "we the people" refers to everyone (not a subset of people).
